Free Printable Testing Series for Convergence/Divergence

1.

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

a)

Converges

b)

Diverges

2.

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

a)

Converges

b)

Diverges

3.

$\sum_{n=1}^{\infty}\frac{6}{4^{3n}}$

a)

Converges

b)

Diverges

4.

$\sum_{n=1}^{\infty}ne^{-n}$

a)

Converges

b)

Diverges

5.

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

a)

Converges

b)

Diverges

6.

$\sum_{n=1}^{\infty}\frac{1}{n^{1.06}}$

a)

Converges

b)

Diverges

7.

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

The series above is a

a)

geometric series

b)

p-series

8.

Let f be a positive, continuous, decreasing function such that

a_n=f\left(n\right)

. If

\sum_{n=1}^{\infty}a_n

converges to k, which of the following must be true?

a)

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

b)

$\int_1^nf\left(x\right)dx=k$

c)

$\int_1^{\infty}f\left(x\right)dx$ diverges

d)

$\int_1^{\infty}f\left(x\right)dx\$ converges

e)

$\int_1^{\infty}f\left(x\right)dx=k$

9.

Which of the following series diverge? (check all that apply)

a)

$\sum_{n=0}^{\infty}\left(\frac{\sin2}{\pi}\right)^n$

b)

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

c)

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

10.

What is the sum of the converging geometric series below?

$\sum_{n=1}^{\infty}\frac{7^{n+1}}{10^n}$

(a)

Testing Series for Convergence/Divergence

Total questions: 10

Worksheet time: 14mins

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