How do I determine the convergence/divergence of the following:
I can't use limit comparison test with because it gives me 0. Root and ratio tests don't seem appropriate and I'm struggling to find a divergent series which is smaller than this to compare it with. Would it be possible to compare it with ?
I'm more or less completely stuck.
Thanks for the help in advance.
You can write
(Because or just (this is the same) because of the usual Taylor expansion of the exponential at zero: )
As a consequence, since diverges, and we deal with series with positive coefficients, you can conclude that your series diverges as well.