Determining Convergence/Divergence Of Infinite Series

[Bashyboy]

Homework Statement

I attached the solution to the problem.

Homework Equations

The Attempt at a Solution

I can see that the infinite series diverges by looking at a few terms, but how would I find a general term for the infinite series, to evaluate it analytically?

 

[jbunniii]

I can see that the infinite series diverges by looking at a few terms, but how would I find a general term for the infinite series, to evaluate it analytically?

If your goal is to prove that the series diverges, you don't necessarily need to find an expression for the general term (by which I assume you mean the n'th partial sum).

There is a very simple test which you should always apply as the first step. If this test fails, the series diverges. What test am I referring to?

 

[Bashyboy]

Would it be the nth term test?

 

[jbunniii]

Yes. What does that test imply for this series?