Write out the first five terms of the sequence \left[{\frac{\left(-1\right)^{n-1}}{\left(n+1\right)^{2}}}\right]_{n=1}^{\infty} , determine whether the sequence converges, and if so find its limit.

Enter the following information for

(Enter DNE if limit Does Not Exist.)

Does the sequence converge

You can earn partial credit on this problem.