sorry, but i am not looking whether the series is converging or not. I know it converges.
Also your condition number 2 is not necessary for an alternating series to converge.
I am interested in proving that the total sum is positive.
I was trying to prove the following but couldn't succeed. Is there a systematic methods to prove that the following infinite sum is positive? (alternating series)
sum from n = 0 to ∞ of ((-1)^{n}* x^{n+z}) / (n+z)!
conditions x≥0 and z≥1
note: when x≤1, we can directly see that s_{n}-...