QJEEAdv03Mae790: JEE Advanced 2003 Mathematics - Class 11 JEEAdv03Mae790 Solution: Prove that 2 k ( n 0 ) ( n k ) − 2 k − 1 ( n 2 ) ( n 1 ) ( n −…

Question

Verified Solution • 2025–26 Session moderate

Prove that

2^{k} (\begin{matrix} n \\ 0 \end{matrix}) (\begin{matrix} n \\ k \end{matrix}) - 2^{^{k - 1} (\begin{matrix} n \\ 2 \end{matrix})} (\begin{matrix} n \\ 1 \end{matrix}) (\begin{matrix} n - 1 \\ k - 1 \end{matrix})

+ 2^{k - 2} (\begin{matrix} n - 2 \\ k - 2 \end{matrix}) - . . . . . {(- 1)}^{k} (\begin{matrix} n \\ k \end{matrix}) (\begin{matrix} n - k \\ 0 \end{matrix}) = {(\begin{matrix} n \\ k \end{matrix})}^{\cdot}

Accepted Answer

Answer

No answer available for this question.