If-the-sum-of-the-coefficients-in-the-expansion-of-1-2x-n-is-6561-then-the-greatest-coefficient-in-the-expansion-is-

Question Number 44315 by Tip Top last updated on 26/Sep/18

If the sum of the coefficients in the

expansion of {(1 + 2 x)}^{n} is 6561, then the

greatest coefficient in the expansion is

Answered by MrW3 last updated on 27/Sep/18

s u m o f a l l c o e f . = {(1 + 2 \times 1)}^{n} = 3^{n}

s u m o f a l l c o e f . = 6561

\Rightarrow 3^{n} = 6561 = 3^{8}

\Rightarrow n = 8

g r e a t e s . c o e f . = C_{5}^{8} \times 2^{5} = 1792

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