Sum of ((-1)^n+1)*((2^n/n^4))

[kilroymcb]

Here is another convergence or divergence problem. On this one, it seems like I would need to use the alternating series test. But, how to satisfy the two conditions of the theorem... first, that the limit goes to zero and the function is decreasing?

 

[skeeter]

does L'Hopital ring a bell?

 

[pka]

the alternating series test. But, how to satisfy the two conditions of the theorem... first, that the limit goes to zero and the function is decreasing?

The sequence \(\displaystyle a_n = \frac{{2^n }}{{n^4 }}\) is neither null (has limit zero) nor is it decreasing for \(\displaystyle n > 10\).