Question

Suppose $\displaystyle\sum_{r=0}^{2023} r^{22023} C_r=2023 \times \alpha \times 2^{2022}$ Then the value of $\alpha$ is

Answer 1

The correct answer is 1012.
using result
r=0∑n​r2nCr​=n(n+1)⋅2n−2
Then r=0∑2023​r22023Cr​=2023×2024×22021
=2023×α×22022 So,
⇒α=1012