Question
If the sum of the coefficients in the expansion of (a +
b)n is 16384, then the greatest coefficient in the expansion isSolution
Binomial expansion: (x + y)n = C0 xn + C1 xn-1 y + C2 xn-2y2 + ….+ Cnyn Putting x = y = 1, we get 2n = C0 + C1 + C2 + ….+ Cn = 16384 = 214 => n = 14 Since n is even here, so the coefficient of greatest term is n Cn/2 = 14C14/2 = 14C7 = 13 × 2 × 11 × 2 × 3 × 2 = 3432
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