Two problems:

1.((infinity) summation (n=1)) (((-1)^n)*(n+2))/(n*(n+1))

Since the top has only one n and the denominator has 2, the fraction will decrease, the limit is 0, and is positive. This converges.

I then used the ratio test to see if this function converges absolutely...

I replaced the n(s) with n+1 and got:

((n+3)*n)/(n+2)^2... I then took the limit when n approaches infinity and got

n^2/n^2 = 1... since 0<1<oo, this converges absolutely. Did I do this right?

2.((infinity) summation (n=1)) (((-1)^k) * n^3)/ (4^n)

The issue with this problem is that I never dealt with a problem with two variable as with this one. If anybody can help me, I will be grateful.