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

$$\mathrm{If}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{coefficients}\mathrm{in}\mathrm{the}$$$$\mathrm{expansion}\mathrm{of}{(1+2x)}^n\mathrm{is}6561,\mathrm{then}\mathrm{the}$$$$\mathrm{greatest}\mathrm{coefficient}\mathrm{in}\mathrm{the}\mathrm{expansion}\mathrm{is}$$

Answered by MrW3 last updated on 27/Sep/18

$$sumofallcoef.={(1+2\times 1)}^n=3^n$$$$sumofallcoef.=6561$$$$\Rightarrow 3^n=6561=3^8$$$$\Rightarrow n=8$$$$greates.coef.=C_5^8\times 2^5=1792$$

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