HMMT 2001 U21

Evaluate $\sum_{i=1}^{\infty} \frac{(i+1)(i+2)(i+3)}{(-2)^{i}}$ .

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.