Series Problems

These questions are meant to be practice problems for series.

Determine whether the series converge or diverge.

Click on the  boxed problem numbers  to go to a solution.

 Problem 1 

$\sum _{n=1}^{\infty }{\frac {2+3^{n}}{4^{n}}}$

 Problem 2 

$\sum _{n=1}^{\infty }\ln {\Bigg (}{\frac {n^{2}+1}{2n^{2}+1}}{\Bigg )}$

 Problem 3 

$\sum _{n=1}^{\infty }{\frac {n}{n^{4}+1}}$

 Problem 4 

$\sum _{n=1}^{\infty }{\frac {n^{2}-1}{3n^{4}+1}}$

 Problem 5 

$\sum _{n=1}^{\infty }{\frac {(-1)^{n-1}n^{2}}{10^{n}}}$

 Problem 6 

$\sum _{n=1}^{\infty }{\frac {10^{n}}{(n+1)4^{2n+1}}}$

 Problem 7 

$\sum _{n=1}^{\infty }{\frac {(n^{2}+1)^{2n}}{(2n^{2}+1)^{n}}}$

 Problem 8 

$\sum _{n=1}^{\infty }{\frac {6n-12}{n^{2}-4n+5}}$ (using the Integral Test)

 Problem 9 

$\sum _{n=1}^{\infty }{\frac {n-1}{n^{2}{\sqrt {n}}}}$

 Problem 10 

$\sum _{n=1}^{\infty }{\frac {\sin({\frac {n\pi }{2}})}{n^{3}}}$

 Problem 11 

$\sum _{n=1}^{\infty }{\frac {3^{n}+4^{n}}{5^{n}}}$

 Problem 12 

$\sum _{n=1}^{\infty }{\frac {n^{2}+1}{5^{n}}}$

 Problem 13 

$\sum _{n=1}^{\infty }{\frac {e^{\frac {1}{n}}}{n^{2}}}$

 Problem 14 

$\sum _{n=1}^{\infty }\sin(n)$

 Problem 15 

$\sum _{n=1}^{\infty }n^{2}e^{-n^{3}}$