MCQ
$2{C_0} + \frac{{{2^2}}}{2}{C_1} + \frac{{{2^3}}}{3}{C_2} + .... + \frac{{{2^{11}}}}{{11}}{C_{10}}$ = . . . 
  • $\frac{{{3^{11}} - 1}}{{11}}$
  • B
    $\frac{{{2^{11}} - 1}}{{11}}$
  • C
    $\frac{{{{11}^3} - 1}}{{11}}$
  • D
    $\frac{{{{11}^2} - 1}}{{11}}$

Answer

Correct option: A.
$\frac{{{3^{11}} - 1}}{{11}}$
a
(a) We have ${(1 + x)^{10}} = {C_0} + {C_1}x + {C_2}{x^2} + ... + {C_{10}}{x^{10}}$

Integrating both sides from $0$ to $2$, we get

$\frac{{{3^{11}} - 1}}{{11}} = 2{C_0} + \frac{{{2^2}}}{2}{C_1} + \frac{{{2^3}}}{3}{C_2} + .... + \frac{{{2^{11}}}}{{11}}{C_{10}}$.

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