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If the sum of the coefficients of $(1+x)^n=4096$, then the largest coefficient is ?

$\begin{array}{1 1} ^{12}C_6 \\ ^{13} C_7 \\ ^{12}C_7 \\ ^{14} C_7\end{array} $

1 Answer

Toolbox:
  • Then highest coeff. out of $^{2n}C_0,^{2n}C_2,.......^{2n}C_{2n}$ is $^{2n}C_n$
  • $^nC_0+^nC_1+.......^nC_n=2^n$
Given: $^nC_0+^nC_1+^nC_2+.......^nC_n=4096$
$\Rightarrow\:2^n=4096$
$\therefore\:n=12$
$\Rightarrow\:$ The highest coefficient is $^{12}C_6$
answered Nov 24, 2013 by rvidyagovindarajan_1
 

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