Binomial TheoremHard

Question

Coefficient of xn - 1 in the expansion of, (x + 3)n + (x + 3)n - 1 (x + 2) + (x + 3)n - 2 (x + 2)2 +..... + (x + 2)n is :

Options

A.n+1C2(3)
B.n-1C2(5)
C.n+1C2(5)
D.nC2(5)

Solution

(x + 3)n + (x + 3)n-1 (x + 2) + ...... + (x + 2)n = (x + 3)n = [(x + 3)n+1 - (x + 2)n+1]
Coefficient of xn-1 = n+1Cn-1 (3)2 - n+1Cn-1 × 4

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