Test whether the sequence converges or diverges.

A(subscript n)=((-1)^(n-1) * n)/(n^+ 1)

I was completely lost in this question, but i attempted anyway

I was able to determine you need to divide numerator and denominator by n isolating (-1)^n-1 on top. I also brought the -1^-1 to the front to simplify things, however, my book didn't do that.

I know you needed to use the squeeze theorem but the (-1)^n threw me off thogh and when i checked my solutions manual (which is poorly laid out for the record) they use the absolute value of A(subscript n) in their squeeze theorem

Using the squeeze theorem they let 0/n = 0< |a(sub n)| = 1/(n+1/n) < 1/n

I understand how this can make sense as the limits of the outer equations both equal 0, making the limit of the inner equation equal 0, but why is it legal to just use 1 (i'm assuming 1 to equal |1^n| in this case) instead of (-1)^n?

Thanks in advance!