Free Printable Review of Convergence Tests

1.

nth term test:

If the limit as n approaches infinity of a series is (a) zero, then the series will diverge.

2.

Geometric Series:

A geometric series will converge if (a) .

3.

Geometric Series:

If a geometric series converges, the sum of the series will be equal to...

a)

$\frac{a_i}{r+1}$

b)

$\frac{a_i}{r-1}$

c)

$\frac{a_i}{1+r}$

d)

$\frac{a_i}{1-r}$

4.

Integral test:

If the integral (a) , then the series converges.

5.

p-series:

A p-series will converge if (a) .

6.

Direct comparison test:
Given that

0<a_n<b_n

select which of the following statements is true.

a)

If $b_n$ diverges, then $a_n$ diverges.

b)

If $b_n$ converges, then $a_n$ converges.

c)

If $a_n$ converges, then $b_n$ converges.

d)

If $a_n$ diverges, then $b_n$ converges.

7.

Limit Comparison Test:
Given that

\lim_{n\rightarrow\infty}\ \frac{a_n}{b_n}=L

, where L is finite and positive, then

a)

$a_n$ and $b_n$ have the same behavior (both converge or both diverge)

b)

$a_n$ and $b_n$ have the opposite behavior (one converges and the other diverges)

8.

Alternating Series Test:
An alternating series will converge if:

\lim_{n\rightarrow\infty}\ a_n=

(a)

9.

Alternating Series Test:
An alternating series will converge if:

a_n+1

(a)

a_n

10.

Ratio Test:
A series will converge by the ratio test if

\lim_{n\rightarrow\infty}\left|\frac{a_{\left(n+1\right)}}{a_n}\right|

(a) 1

11.

Will the series converge or diverge?

\sum_{n=1}^{\infty}\frac{n!}{n\cdot3^n}

a)

converge

b)

diverge

12.

Will the series converge or diverge?

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

a)

converge

b)

diverge

13.

Will the series converge or diverge?

\sum_{n=1}^{\infty}\frac{\sqrt{3n-4}}{\sqrt{9n+2}}

a)

converge

b)

diverge

14.

Will the series converge or diverge?

\sum_{n=1}^{\infty}\frac{3^n}{8^{\left(n+1\right)}}

a)

converge

b)

diverge

15.

Will the series converge or diverge?

\sum_{n=1}^{\infty}\frac{n^{\frac{2}{3}}}{n^{\frac{13}{3}}}

a)

converge

b)

diverge

16.

Will the series converge or diverge?

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

a)

converge

b)

diverge

17.

Will the series converge or diverge?

\sum_{n=1}^{\infty}\left(-1\right)^n\cdot\frac{e^n}{\sqrt{n}}

a)

converge

b)

diverge

18.

Will the series converge or diverge?

\sum_{n=1}^{\infty}n\cdot e^{-n^2}

a)

converge

b)

diverge

19.

The function f is defined by

f\left(x\right)=\sum_{n=0}^{\infty}\left(\frac{x}{3}\right)^n

What is the value of f(1)?
Enter your answer as a fraction in simplest form.

(a)

20.

What is the value of

\sum_{n=1}^{\infty}\frac{7^n}{10^{\left(n+1\right)}}

Enter your answer as a fraction in simplest form.

(a)

Review of Convergence Tests

Total questions: 20

Worksheet time: 37mins

Similar Resources on Wayground