Solution of Problem 4 - Ratio Test

We use the :

lim
n® ¥ 
 | an+1|
| an|
=
lim
n® ¥ 
 2n+1
n+2
 n+1
2n
 = 2
lim
n® ¥ 
 n+1
n+2
 = 2
 > 1
Therefore the series diverges.

Note that this problem can also be solved using the n-th Term Test.