Unit 10A Review

• Converge

• Diverge

Does the series $\sum_{n=1}^{\infty}\frac{3n}{2n-1}$ converge or diverge? 

• Converge

• Diverge

What conclusion can you make using the nth term test to describe

 $\sum_{n=1}^{\infty}\frac{6n}{4n^2+1}$  

• This series diverges by the nth term test

• This series converges by the nth term test

• No conclusion about this series can be made using the nth term test.

Determine the convergence/divergence of the series

 $\sum_{n=1}^{\infty}\frac{2^n}{5^{n+1}}$  and find the sum (if possible).

• This series diverges

• This series converges to  $\frac{2}{15}$  

• This series converges but we cannot find the sum

• This series converges to  $\frac{2}{25}$  

Tags

CCSS.HSA.APR.D.7

CCSS.HSF.LE.A.1

• Diverges

• This converges, but we cannot find the sum

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Which of the following series diverge?

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

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

•  $\sum_{n=1}^{\infty}\frac{n^6}{n^7}$  

•  $\sum_{n=1}^{\infty}\frac{n^7}{n^6}$  

Determine the convergence/divergence of the series

 $3-\frac{9}{2}+\frac{27}{4}-\frac{81}{8}+...$  and find the sum (if possible).

• This series diverges

• This series converges to  $\frac{6}{5}$  

• This series converges but we cannot find the sum

• This series converges to 6

How many terms of the series $\sum_{n=1}^{\infty}\left(-1\right)^{n+1}\frac{1}{n^4}$ are needed to approximate the sum of the series with an error less than 0.001? 

• 3

• 4

• 5

• 6

If the series $\sum_{n=1}^{\infty}\frac{1}{n^{1.01}}$ converges, which of the following series also converges by the direct comparison test? 

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

•  $\sum_{n=1}^{\infty}\frac{1}{n^{1.01}-1}$  

•  $\sum_{n=1}^{\infty}\frac{1}{n^{0.99}}$  

•  $\sum_{n=1}^{\infty}\frac{1}{n^{1.01}+1}$  

• Diverges

• Converges but we can't find the sum

• 1