Evaluate the infinite series:
[tex] \displaystyle \large{ \sum_{n = 1}^{ \infty} \frac{1}{(n + 1) \sqrt{n} + n \sqrt{n + 1} } }[/tex]
Please show your work too — thanks!
Answers
9514 1404 393
Answer:
sum = 1
Step-by-step explanation:
The method of partial sums has you look at sums of various numbers of terms of the series to see if there is a pattern that suggests either divergence or a limit. Here, the partial sums suggest the series sum is 1.
__
In the attachment, we have computed sums of 1 term, 10 terms, 100 terms, and so on up to 10^8 terms. These sums seem to approach the value 1.
Individual terms get small faster than for a harmonic series, which his known not to converge, but more slowly than a quadratic series. Large numbered terms are approximately proportional to n^-(3/2).
_____
You can actually compute the sum exactly, without reference to partial sums. Each term of the sum can be rewritten as ...
[tex]\dfrac{1}{(n+1)\sqrt{n}+n\sqrt{n+1}}=\dfrac{1}{\sqrt{n(n+1)}(\sqrt{n+1}+\sqrt{n})}\\\\=\dfrac{\sqrt{n+1}-\sqrt{n}}{\sqrt{n(n+1)}}=\dfrac{1}{\sqrt{n}}-\dfrac{1}{\sqrt{n+1}}[/tex]
Then successive terms will cancel the intermediate fractions. So, for example, the sum of the first 3 terms is ...
(1/√1 -1/√2) +(1/√2 -1/√3) +(1/√3 -1/√4) = 1 -1/√4
This means the given sum will evaluate to ...
1 -1/√∞ = 1 -0 = 1 . . . sum of the infinite series
![Evaluate The Infinite Series:[tex] \displaystyle \large{ \sum_{n = 1}^{ \infty} \frac{1}{(n + 1) \sqrt{n}](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/rpEP4lZYdhvGbef8Dwf3bhCYcpZPENPh.png)
Related Questions
pythagorean theorem help meeeeee!!
Answers
Answer:
25
Step-by-step explanation:
remember that the pythagorean theorem is a²+b²=c²
so this equation would be:
7²+24²=c²
solve the exponents
49 + 576 = c²
combine like terms
625 = c²
take the radical of each number
√625 = √c²
25 = c
have a lovely day <3
...NO LINKS IF YOU HAVE LINK DO NOT ANSWER PLEASE ANSWER NO LINKS Please no links will mark brainiest for complete and correct answer.
PLEASE SHOW ALL OF YOUR WORK
Solve for p
3(2p−1)−2(3p+4)=11p
Answers
Answer:
P = -1
Step-by-step explanation:
3(2p-1)-2(3p+4)=11p
Distribute:
6p-3-6p-8=11p
Combine like terms:
-11 = 11p
Solve for p by dividing by 11:
-11/11 = 11p/11
Simplify:
-1 = p
Step-by-step explanation:
6p - 3 - 6p - 8 = 11p
-11 = 11p
p = -1
Giving me brainiest will be appreciated
I WILL GIVE BRAINLESS) Math Journal Write a word problem that involves a proportional relationship and needs more than one step to solve. Show how to solve the problem. 1
Answers
Answer:
565.48 sq. in.
Step-by-step explanation:
Given the Slant height and radius, we are asked to find the lateral area of the cone.
Lateral area of the cone is given by
where, 'r' is the radius of the cone.
and 'l' is its slant height.
From the figure, we see that the slant height of the cone, l = 15 in
Also, the radius of the cone, r = 12 in.
Therefore,
= 565. 48 sq. in. which is the required answer.
Answer:
A proportional relationship is written as:
y = k*x
where k is the constant of proportionality.
A general word problem that represents one of these relationships can be:
If each burger costs $1.50, what would be the cost of buying x burgers?
The cost of x burgers will be x times $1.50, so if we define y as the total price, we will have the relation:
y = $1.50*x
Which is a proportional relationship where the constant of proportionality is $1,50
Evaluate -(2")(2º).
A.1/8
B. -8
C. 8
D.-1/8
Answers
Answer:
= -8
(hope this helps) :)
what is this problem please help70^1/3
Answers
Answer:
23.333....
Step-by-step explanation:
PLEASE HELP
Absolute Value Inequalities
Answers
Plz answer this question
Answers
I believe the answer is B 3/4
THIS IS NOT A SCAM LINK ITS REAL
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A farmer owns a total of 8 acres of land. The land is separated into (3)1/3 equally sized sections. How many acres are in each section?
Write your answer as a mixed number in simplest form.
Answers
Answer:
each section is 2 2/3 or 2.66666666
Step-by-step explanation:
The circumference of a circle is just ?
Answers
Answer:
The formula is C = πd
π = pie
d= diameter
C =circumference
Answer:
C = 2πr
Step-by-step explanation:
C = 2πr
where C = circumference,
π = pi = 3.14159...,
and r = radius of the circle.
The rectangular frame is made from 5 straight pieces of metal.
6 m
8 m
The weight of the metal is 1.5 kg per metre.
Work out the total weight of the metal in the frame.
Answers
Step-by-step explanation:
the perimeter = 2×(8+6)
= 2(14) = 28m
the diagonal = √8²+6²
= √64+36
=√100 = 10m
the total length of the frame =
28+10 = 38 m
therefore the total Weight =
38× 1.5 kg = 57 kg
The correct answer is 57kg.
the perimeter = 2×(8+6)
= 2(14) = 28m
the diagonal = √8²+6²
= √64+36
100 = 10m
the total length of the frame =
28+10 = 38 m
therefore the total Weight =
38× 1.5 kg = 57 kg
What is the weight formula?The weight of an object is defined as the force of gravity on the object and may be calculated as the mass times the acceleration of gravity, w = mg.
To obtain the weight of your metal, you will multiply the sectional area, length and density together. Then, to convert the weight to kilograms, you must divide the product by 1,000. You can also determine the weight of your metal product using any number of online metal weight calculators.
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What is 3/4+1/4+1/2=
Answers
Answer:
3/2
Step-by-step explanation:
Answer:
Exact Form: [tex]\frac{3}{2}[/tex]
Decimal Form: 1.5
Mixed Number Form: [tex]1\frac{1}{2}[/tex]
Step-by-step explanation:
In pic
(Credits: Symbolab)
(Hope this helps can I pls have brainlist (crown)☺️)
Which equation is equivalent to 0.3y +0.4(25 - y) = 6.8 ?
Answers
Answer
y = 32
Step-by-step explanation:
Let's solve your equation step-by-step.
0.3y+0.4(25−y)=6.8
Step 1: Simplify both sides of the equation.
0.3y+0.4(25−y)=6.8
0.3y+(0.4)(25)+(0.4)(−[tex]\frac{-0.1y}{-0.1} =\frac{-3.2}{-0.1}[/tex]y)=6.8(Distribute)
0.3y+10+−0.4y=6.8
(0.3y+−0.4y)+(10)=6.8(Combine Like Terms)
−0.1y+10=6.8
−0.1y+10=6.8
Step 2: Subtract 10 from both sides.
−0.1y+10−10=6.8−10
−0.1y=−3.2
Step 3: Divide both sides by -0.1.
-0.1y/-0.1=-3.2/-0.1
y=32
I hope this helps?
A reason improper use of netiquette can be risky is that users can
O become vulnerable to online harassment.
O access inappropriate websites.
O have their private information stolen.
O receive unwanted spam.
Answers
The answer is A, Sorry I am late but for the future people i hope this helps them :))
- Have a nice day.
The improper use of netiquette can be risky as the user can become vulnerable to online harassment.
What is cybersecurity?Protecting the online data from the digital attacks initiated by a hacker is called cybersecurity. Cybersecurity is necessary to protect the various systems, networks and programs that may contain some confidential information about any person.
Given is to identify the reason why the improper use of netiquette can be risky.
The improper use of netiquette can be risky as the user can become vulnerable to online harassment.
Therefore, the improper use of netiquette can be risky as the user can become vulnerable to online harassment.
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In the inequality 4>-4, which number appears farther right on a number
line and why?
O A. -4 appears farther right because -4 is smaller than 4.
O B. -4 appears farther right because - 4 is larger than 4.
C. 4 appears farther right because 4 is larger than -4.
D. 4 appears farther right because 4 is smaller than -4.
PLEASE HELP ASAP!! THIS IS ONE OF MY FINAL TEST… AKA- ITS MOST OF MY GRADE
Answers
Answer:
"C" 4 appears farther right because 4 is larger than -4.
A pet store has 15 birds and 75 fish.
In simplest form, what is the ratio of birds to fish in the pet store?
O1/6
O1/5
O5/1
I don't know
Answers
Answer:
1/5
Step-by-step explanation:
For every bird in the store there will be 5 fish.
Because there is 5 times more fish then birds.
Using the ratio concept, the number of birds to fish expressed as a ratio is 1/5
Given the Parameters :
Number of birds = 15 Number of fishes = 75Ratio of the number of birds to fish can be expressed thus :
Number of birds : Number of fishes15 : 75
Divide both sides by 15
1 : 5
Hence, the ratio of birds to fish is 1/5
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ΔABC is similar to ΔDEF. The length of segment AC is 12 cm. The length of segment BC is 18 cm. The length of segment DF is 10 cm.
What is the length of segment EF?
Question 1 options:
15
14
10
9
Answers
Answer:
It's 15
i took the test
Step-by-step explanation:
Solve 2x^2-3x-5=0 with the quadratic formula please and have a bless day
Answers
Answer:
( 2x^62- 3x) - 5 = 0
2x^62 - 3x - 5 = 0
X = - 1
- 5/2
The it is my dear friend
Name two triangles that are congruent by the ASA Postulate.
ATC=DOG
ATC=NFI
PQR=INF
PQR=IFN
Answers
Answer:
ATC is congruent to DOG by ASA axiom for congruency
Answer: ATC = DOG
Step-by-step explanation:
let x=-(2/5 ) and y= -(1/10)Which expression has a negetive value?A. x+y B. x-y
Answers
Answer: Terminology for signs. When 0 is said to be neither positive nor negative, the following phrases may be used to refer to the sign of a number: A number is positive if it is greater than zero. A number is negative if it is less than zero.
Step-by-step explanation:
Hope this helps!
Let f(x)=5x^4 and g(x)=e^2x+x. If h is the function defined by h(x)=f(g(x)), which of the following gives a correct expression for h′(x)?
Answers
The values of h'(x) is h'(x) = 20 [tex](e^{2x} + x) ^{3}[/tex] (2[tex]e^{2x}[/tex] + 1 ).
Option C is the correct answer.
Given,
f(x)=5x^4 and g(x)=e^2x+x.
If h is the function defined by h(x)=f(g(x)),
We need to find h′(x).
What is the differentiation formula for the following?We have,
dx/dx = 1
d[tex]x^{n}[/tex]/dx = n[tex]x^{n-1}[/tex]
d[tex]e^{x}[/tex]/dx = [tex]e^{x}[/tex]
d[tex]e^{n}[/tex]/dx = [tex]ne^{n}[/tex]
d(cx)/dx = c(dx/dx) = c
We have,
- f(x)=5[tex]x^{4}[/tex] ______(1)
- g(x)=[tex]e^{2x}[/tex]+x ______(2)
- h(x)=f(g(x)) _______(3)
Now,
h(x) = f ( [tex]e^{2x}[/tex]+x )
From (1)
h(x) = 5[tex](e^{2x} + x) ^{4}[/tex] ______(4)
Now,
Differentiate (4)
h'(x) = 5 d[tex](e^{2x} + x) ^{4}[/tex]/dx
h'(x) = 5 x 4 [tex](e^{2x} + x) ^{3}[/tex] d [tex](e^{2x} + x)[/tex] / dx
h'(x) =20 [tex](e^{2x} + x) ^{3}[/tex] ( d[tex]e^{2x}[/tex]/dx + dx/dx )
h'(x) = 20 [tex](e^{2x} + x) ^{3}[/tex] (2[tex]e^{2x}[/tex] + 1 )
Thus the values of h'(x) is h'(x) = 20 [tex](e^{2x} + x) ^{3}[/tex] (2[tex]e^{2x}[/tex] + 1 ).
Option C is the correct answer.
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simplify the problem 4 . 3 + 1 . 6 + 8 . 4 − 0 . 9
Answers
Answer:
13.4
Step-by-step explanation:
4.3+1.6=5.9
5.9+8.4=14.3
14.3-0.9=13.4
a room has a rectangular floor that measures 28 feet by 14 feet and a flat 9-foot ceiling. what is the area of the floor and how much air does the room hold?
Answers
Answer:
Step-by-step explanation:
Solve 5x + 2 = 22
Solve 2x-5=7
Solve 2x+5=12
Answers
Answer:
x = 4
x = 6
x = 7/2
Step-by-step explanation:
Solve 5x + 2 = 22:
5x+2-2=22-2 (subtract 2 from both sides)
5x=20
x=4
Solve 2x-5=7
2x-5+5=7+5 (add 5 to both sides)
2x=12
x=6
Solve 2x+5=12
2x+5-5=12-5 (subtract 5 from both sides)
2x=7
x= 7/2
=> 5x + 2 = 22
=> 5x = 22 – 2
=> 5x = 20
=> x = 20/5
=> x = 4
Solve 2x-5=7=> 2x - 5 = 7
=> 2x = 7+5
=> 2x = 12
=> x = 12/2
=> x = 6
Solve 2x+5=12=> 2x + 5 = 12
=> 2x = 12-5
=> 2x = 7
=> x = 7/2
If there are 5 females in a classroom, and 4 males, but 4 of the females are students, whos the other female? please only answer if you know ive been stuck on this for hours
Answers
Answer:
1 teacher female
Step-by-step explanation:
Answer:
Teacher?
Step-by-step explanation:
Well if the other female isn't a student then it must be the teacher.
The measure of an angle is 15.8°. What is the measure of its complementary angle?
Answers
Answer:
x = 74.2°
Step-by-step explanation:
Complementary angles are two angles whose sum is 90°.
Let x = the second angle
15.8° + x = 90°
x = 90 - 15.8°
x = 74.2°
14. A customer's cell phone bill cost $60.50. The company charges a monthly fee of $28 plus
five cents for each minute. Create and solve an equation for the number of minutes the
customer spent talking on the phone. Let m represent the number of minutes.
Answers
your work is not complete
HELP ASAP 100 POINTS!!
Is this graph a function?
This cannot be determined from this graph.
This is a function.
This is not a function.
Answers
Answer:
Sorry but.
Step-by-step explanation:
Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
1. How has the cost of a movie ticket changed over the last 30 years? What has been the general trend? How can you tell this from the graph? (2 points)
2. What years did the cost of movie ticket decrease compared to the year before? How can you tell from the graph when the price is decreasing? (2 points)
Student Name:
Predicting Movie Ticket Costs Activity
3. There was a time where the cost of a movie ticket stayed relatively the same over several years. For what years did the cost stay relatively the same? How can you tell this from the graph? (2 points)
4. The graph could be divided up into three different periods of relatively consistent ticket price change: The years 1980 – 1988, 1989 – 1993 and 1994 – 2011. Can you find a typical rate of change in the price of a ticket for each of these time periods? In other words, on average, by how much did the price of a ticket increase by each year during each of these time periods? (2 points)
5. Predict the cost of a ticket in 2012 – 2015. Plot your predictions and give your actual predictions for each year below. How did you determine how much a ticket would cost each year? (2 points)
6. What might have been the cost of a ticket during the years 1975 – 1979? Plot your estimates on the grid and give your actual predictions for each year below. How did you determine how much a ticket would cost each year? (2 points)
Student Name:
Predicting Movie Ticket Costs Activity
7. Find a line of best fit to represent the data. Let y = ticket price and x = the number of years since 1980 (1980 is year zero, 1981 is year one). Approximate a line to represent the data, a slope, a y- intercept and equation that models your line of best fit. (2 points)
8. Use your equation (or graph or a table) to predict the cost of a movie ticket in the years 2020 and 2030. Be sure to show how you came to each answer. (2 points)
Answers
Answer:
1. For most of the 1990s, tickets sold for an average of less than $5 apiece, and dating back to the 1960s, many Americans could go to the movies for less than a buck. 24/7 Wall St. reviewed data from the National Association of Theatre Owners to determine the cost of a movie ticket the year you were born. A full-price AMC ticket is averages $10.50 nationwide, reflecting a 50-cent increase. Concession prices also increased.
Your asking alot for 50 points so i did 1..
Step-by-step explanation:
2. The price of a gallon of gas was $2.95 on Monday. On Wednesday, the price of a gallon of gas rose to $3.15. How much did the price rise?
The amount of $ by which the price increased
Help
Answers
Answer:
0.2
Step-by-step explanation:
2.95-3.15
Inverse operation for 6*8=48