Compute $\displaystyle \sum_{n=2}^\infty \sum_{k=1}^{n-1} \frac{k}{2^{n+k}}$.
Question:
Compute $\displaystyle \sum_{n=2}^\infty \sum_{k=1}^{n-1} \frac{k}{2^{n+k}}$.
Answer:
Let's think step by step.

user
\frac{4}{9}
Compute $\displaystyle \sum_{n=2}^\infty \sum_{k=1}^{n-1} \frac{k}{2^{n+k}}$.
train