C_0+2 C_1+3 C_2+ +(n+1) C_n =? - Vidyadip

MCQ

$\left\{C_0+2 C_1+3 C_2+\ldots+(n+1) C_n\right\}=?$

A
$( n +1). 2^{ n }$
B
$( n +2) . 2^{ n +1}$
C
$( n +2). 2^{ n -1}$
D
$n . 2^{ n -1}$

✓

Answer

(c) $( n +2) . 2^{ n -1}$
Explanation: Here, $C _0+2 C _1+3 C _2+\ldots+( n +1) C _{ n }$
$\begin{array}{l}=\left(C_0+C_1+C_2+\ldots+C_n\right)+\left(C_1+2 C_2+3 C_3+\ldots+n C_n\right) \\
=2^n+n \cdot 2^{n-1}=(n+2) \cdot 2^{n-1}\end{array}$

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