Summation of infinite series

Question

Find $\frac{3}{2^2(1)(2)}$ + $\frac{4}{2^3(2)(3)}$ +....+ $\frac{r+2}{2^{r+1}(r)(r+1)} +.... up to infinity.

Answer 1

1/2: We will prove that 1/2 is upper limit to the sum.

Here is a link to the article:

https://www.wyzant.com/resources/files/591102/upper_limit_of_infinite_sum