The expression given is:
$$\lim_{N\to\infty}\sum_{k=1}^N \frac{2M}{3N}*(\frac{2}{3} - (\frac{2}{3N})^k)$$
I was able to compute the limit and arrive at:
$$\frac{4M}{9}$$
Does this amount to integrating the function from 1 to infinity? If so how do I not integrate but extract the function? How do I know the function from this Riemann Sum?