Free Printable Topics 10.0-10.4 Review

1.

Determine whether the SEQUENCE converges or diverges. If the sequence converges, find the limit of the terms.

$a_n=\sqrt{\frac{1+4n^2}{n^2}}$

a)

Diverges

b)

2

c)

4

d)

1

2.

Determine whether the SEQUENCE converges or diverges. If the sequence converges, find the limit of the terms.

$a_n=\cos\left(\frac{n\pi}{n+1}\right)$

a)

Diverges

b)

0

c)

1

d)

-1

3.

Determine whether the SEQUENCE converges or diverges. If the sequence converges, find the limit of the terms.

$a_n=n^2e^{-n}$

a)

Diverges

b)

0

c)

1

d)

e

4.

Determine whether the SEQUENCE converges or diverges. If the sequence converges, find the limit of the terms.

$a_n=\ln\left(n+1\right)-\ln\left(n\right)$

a)

Diverges

b)

0

c)

1

d)

e

5.

Determine whether the SEQUENCE converges or diverges. If the sequence converges, find the limit of the terms.

$a_n=\frac{n^2}{\sqrt{n^3-2n}}$

a)

Diverges

b)

0

c)

1

d)

1/2

6.

Which of the following SEQUENCES does not converge?

a)

$a_n=\frac{3n}{2n+1}$

b)

$a_n=\frac{n\ln n}{n^2+1}$

c)

$a_n=\frac{\sqrt{n+1}}{n}$

d)

$a_n=\frac{2^n}{n^3+1}$

7.

If $a_n=1-\frac{n+1}{n}$ , then $\sum_{n=1}^{\infty}a_n$ converges by the nth term test.

a)

True

b)

False

8.

If $\sum_{n=1}^{\infty}a_n=c$ , where c is a constant, then $\lim_{x\rightarrow\infty}a_n=c$

a)

True

b)

False

9.

The sum of $-\frac{2}{3}+\frac{4}{27}-\frac{8}{243}+...$ is

a)

$\frac{6}{7}$

b)

$\frac{9}{11}$

c)

$-\frac{6}{11}$

d)

Divergent

10.

$\sum_{k=1}^{\infty}\frac{k^2}{k^2-2k+5}$

a)

Converges by the nth term test

b)

Diverges by the nth term test

c)

Inconclusive by the nth term test

11.

$\sum_{n=1}^{\infty}\frac{1}{n^{\frac{1}{3}}}$

a)

Converges by nth term test

b)

Diverges by nth term test

c)

Converges by geo series test

d)

Diverges by geo series test

e)

Inconclusive by nth term test

12.

$\sum_{n=1}^{\infty}\frac{5}{\pi^n}$

a)

Diverges

b)

Converges to $\frac{5}{\pi-1}$

c)

Converges to $\frac{5\pi}{\pi-1}$

d)

Converges but the sum can't be found

13.

$\sum_{n=1}^{\infty}\frac{\left(-3\right)^{n-1}}{4^n}$

a)

Diverges

b)

Converges to $\frac{1}{7}$

c)

Converges to $-\frac{4}{21}$

d)

Converges but the sum can't be found

14.

$\sum_{n=0}^{\infty}\frac{3^{n+1}}{\left(-2\right)^n}$

a)

Diverges

b)

Converges to $\frac{6}{5}$

c)

Converges to $-\frac{5}{9}$

d)

Converges but the sum can't be found

15.

$\sum_{n=1}^{\infty}\frac{e^{2n}}{6^{n-1}}$

Note $e^2\approx7.389$

a)

Diverges

b)

Converges to $\frac{6e^2}{6-e^2}$

c)

Converges to $\frac{36}{6-e^2}$

d)

Converges but the sum can't be found

16.

$\sum_{n=1}^{\infty}\frac{6\cdot2^{2n-1}}{3^n}$

a)

Diverges

b)

Converges to 9

c)

Converges to $\frac{4}{9}$

d)

Converges but the sum can't be found

17.

$\sum_{n=1}^{\infty}3^{n+1}\cdot4^{-n}$

a)

Diverges by the nth term test

b)

Converges by the nth term test

c)

Diverges by the geometric series test

d)

Converges by the geometric series test

18.

$\sum_{n=1}^{\infty}\frac{2^n+4^n}{e^n}$

a)

Diverges

b)

Converges

19.

$\sum_{k=0}^{\infty}\left(\sqrt{2}\right)^{-k}$

a)

Diverges by the geometric series test

b)

Converges by the geometric series test

c)

Diverges by the nth term test

d)

Converges by the nth term test

20.

Use partial fraction decomposition to find the sum of the telescoping series

\sum_{n=2}^{\infty}\frac{2}{n^2-1}

a)

$\frac{3}{2}$

b)

$\frac{7}{6}$

c)

$\frac{1}{6}$

d)

$\frac{11}{12}$

21.

If the sum of the first n terms of the series $\sum_{k=1}^{\infty}a_k$ is $S_n=\frac{2n^2}{3n^2+4}$ , what is the sum of the series?

a)

$\frac{1}{3}$

b)

$\frac{1}{2}$

c)

$\frac{2}{3}$

d)

$\infty$

22.

Which of these series converges to 8?

a)

$\sum_{n=1}^{\infty}\frac{8n}{n+8}$

b)

$\sum_{n=0}^{\infty}\frac{6}{4^n}$

c)

$\sum_{n=0}^{\infty}\frac{8}{n}$

23.

If a>1, then which statement about the series $\sum_{n=0}^{\infty}a^{-n}$ is true?

a)

The series converges to $\frac{a}{a-1}$

b)

The series converges to $\frac{a-1}{a}$

c)

The series converges to $\frac{a}{a+1}$

d)

The series diverges

24.

For which values(s) of x will the series $\sum_{n=0}^{\infty}\frac{1}{2}x\left(2x^2\right)^n$ converge to 3?

a)

$\frac{2}{3}$

b)

$-\frac{3}{4}$

c)

Both $\frac{2}{3}$ and $-\frac{3}{4}$

d)

Netiher $\frac{2}{3}$ or $-\frac{3}{4}$

25.

What is the value of the infinite series $\sum_{n=1}^{\infty}\frac{10\cdot3^n+15\cdot2^n}{5^n}$

a)

0

b)

25

c)

50

d)

$\frac{125}{4}$

26.

Which of the following series diverge by the nth term test?

a)

$\sum_{n=1}^{\infty}\frac{10}{n^2+1}$

b)

$\sum_{n=1}^{\infty}\frac{n^2}{e^n+1}$

c)

$\sum_{n=1}^{\infty}\frac{1}{n}$

d)

$\sum_{n=1}^{\infty}\frac{en}{3n+1}$

27.

Use the integral test to determine convergence or divergence of $\sum_{n=1}^{\infty}\frac{1}{\left(3n-1\right)^4}$

a)

Converges

b)

Diverges

28.

$\sum_{n=1}^{\infty}\frac{\sqrt{n}+4}{n^2}$

a)

nth term test inconclusive

b)

Converges by nth term test

c)

Diverges by nth term test

29.

$\sum_{n=1}^{\infty}\frac{\sqrt{n}}{1+n^{\frac{3}{2}}}$

Determine if the series is convergent or divergent

a)

Converges by nth term test

b)

Diverges by nth term test

c)

Converges by integral test

d)

Diverges by integral test

30.

$1+\frac{1}{2\sqrt{2}}+\frac{1}{3\sqrt{3}}+\frac{1}{4\sqrt{4}}+...$

Determine if the series is convergent or divergent

a)

Converges by integral test

b)

Diverges by integral test

c)

Converges by geometric series test

d)

Diverges by geometric series test

31.

Which of the following series diverge?

a)

$\sum_{n=1}^{\infty}\frac{0.05n}{20n+3}$

b)

$\sum_{n=1}^{\infty}\left(\frac{e}{\sin\frac{\pi}{4}}\right)^n$

c)

$\sum_{n=1}^{\infty}\frac{n!}{n^{20}+1}$

32.

$\sum_{n=1}^{\infty}\frac{1}{n+5}$

a)

Diverges due to nth term test

b)

Converges due to nth term test

c)

Inconclusive due to nth term test

d)

Converges due to integral test

e)

Diverges due to integral test

33.

$\sum_{n=0}^{\infty}e^{-n}$

a)

Diverges due to geo series test

b)

Converges due to geo series test

c)

Converges due to integral test

d)

Diverges due to integral test

34.

$\sum_{n=1}^{\infty}ne^{-n}$ converges due to the integral test. What value is the high bound according to this test?

a)

$\frac{2}{e}$

b)

$e^2$

c)

$\frac{1}{e}$

d)

$e$

35.

$\sum_{n=1}^{\infty}\frac{4}{n^2+1}$ converges due to the integral test. What value does this sum have to be less than according to this test?

a)

$\pi$

b)

$\frac{\pi}{4}$

c)

$\frac{3\pi}{4}$

d)

1

36.

$\sum_{n=1}^{\infty}\frac{8}{n^4}$

a)

Diverges due to nth term test

b)

Converges due to nth term test

c)

Inconclusive due to nth term test

d)

Converges due to integral test

e)

Diverges due to integral test

37.

$\sum_{n=1}^{\infty}\frac{8n!+12^n}{n^{40}-12^n}$

a)

Diverges due to nth term test

b)

Converges due to nth term test

c)

Inconclusive due to nth term test

38.

$\sum_{n=1}^{\infty}\frac{8n+5^{2n}}{n^{10}-30^n}$

a)

Diverges due to nth term test

b)

Converges due to nth term test

c)

Inconclusive due to nth term test

39.

What is the 5th partial sum of $\sum_{k=1}^{\infty}2^{n-1}$ ?

a)

31

b)

62

c)

16

d)

32

40.

It is known that $a_k=\sqrt[]{k+1}-\sqrt[]{k}=\frac{1}{\sqrt[]{k+1}+\sqrt[]{k}}$ . Which of the following is true about $\sum_{k=1}^{\infty}a_k$ ?

a)

$\lim_{k\rightarrow\infty}a_k=0$ and $\sum_{k=1}^{\infty}a_k$ converges

b)

$\lim_{k\rightarrow\infty}a_k=0$ and $\sum_{k=1}^{\infty}a_k$ diverges

c)

$\lim_{k\rightarrow\infty}a_k\ne0$ and $\sum_{k=1}^{\infty}a_k$ converges

d)

$\lim_{k\rightarrow\infty}a_k\ne0$ and $\sum_{k=1}^{\infty}a_k$ diverges

Topics 10.0-10.4 Review

Total questions: 40

Worksheet time: 1hrs 20mins

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