If-the-sum-of-the-coefficients-in-the-expansion-of-a-b-n-is-4096-then-the-greatest-coefficient-in-the-expansion-is-

Tinku Tara June 14, 2023 None 0 Comments

Question Number 9421 by 8168 last updated on 07/Dec/16

If the sum of the coefficients in the expansion of (a+b)^n is 4096, then the greatest coefficient in the expansion is

$$\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{coefficients}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left({a}+{b}\right)^{{n}} \:\mathrm{is}\:\mathrm{4096},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{is} \\ $$

Answered by sandy_suhendra last updated on 08/Dec/16

if the sum of coefficients = 4096 so 2^n = 4096 ⇒ n = 12 the greatest coefficient will be = 12C6 = 924

$$\mathrm{if}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{coefficients}\:=\:\mathrm{4096}\: \\ $$$$\mathrm{so}\:\mathrm{2}^{\mathrm{n}} \:=\:\mathrm{4096}\:\Rightarrow\:\mathrm{n}\:=\:\mathrm{12} \\ $$$$\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{will}\:\mathrm{be}\:=\:\mathrm{12C6}\:=\:\mathrm{924} \\ $$

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