# Analysis - Series

• Apr 20th 2010, 10:26 AM
asingh88
Analysis - Series
The question is i need to prove the following series converge or diverge,
for the first part i get (e^-3+5)/5 which is bigger than 1 so it diverges and for the second part i get 1 ( so is this wrong as a series diverges if it is less than 1 and converges if it is more than 1,or is it a special case)

Any help would be much appreciated
• Apr 20th 2010, 11:16 AM
tonio
Quote:

Originally Posted by asingh88
The question is i need to prove the following series converge or diverge,
for the first part i get (e^-3+5)/5 which is bigger than 1 so it diverges and for the second part i get 1 ( so is this wrong as a series diverges if it is less than 1 and converges if it is more than 1,or is it a special case)

Any help would be much appreciated

$\displaystyle \frac{e^{-3n}}{(2n)^n+5}\leq \frac{1}{2^n}$

$\displaystyle \frac{5n}{n^3+n^2}=\frac{5}{n^2+n}\leq \frac{5}{n^2}$

Now use the comparison test and we're through.

Tonio