Binomial TheoremHard

Question

The co-efficient of x5 in the expansion of (1 + x)21 + (1 + x)22 +....... + (1 + x)30 is :

Options

A.51C5
B.9C5
C.31C6 - 21C6
D.30C5 + 20C5

Solution

(1 + x)21 [1 + (1 + x) + ...... (1 + x)9] = (1 + x)21
Coefficient of x5 = 31C6  - 21C6

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