Hello folks. First off i want to say this is an awesome forum! But lets get to the topic:

I totally understand the concept of convergence/divergence and i dont have problems to follow the lessons. But....

when it comes down to exercises/exams i totally fail in showing wether a series/sequence converges or not

for example:

i got the series: $\displaystyle \sum_{n=1}^{\inf}\frac{cos(4n)}{n}$

my thinking was... finding a series a_n greater than the given one and then proof its convergence. but i seem to fail ....

another typical problem would be:

$\displaystyle lim(1+\frac{2}{n})^{4n}$ testing for convergence as n goes to infinity

my thought was writing the 1 as $\displaystyle \frac{n}{n}$ and then have $\displaystyle \frac{2+n}{n}$ raised to the power of 4n

but to be honest... im lost !