Binomial Theorem
Sum involving $r^2\cdot{}^nC_r$
nta_pyq_2023_jan
Grade 11
Question:
Suppose $\displaystyle\sum_{r=0}^{2023}r^2\cdot{}^{2023}C_r=2023\times\alpha\times2^{2022}$. Then the value of $\alpha$ is ___.
Step-by-Step Solution
Key Concept: Use identity $\sum_{r=0}^n r^2\,{}^nC_r = n(n+1)\cdot2^{n-2}$.
$\alpha=1012$.
Correct Answer: 1012