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The coefficent of x^5 in (1 + 2x + 3x^2 + ....)^3/2 is

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The coefficent of x5 in (1 + 2x + 3x2 + ....)3/2 is 

(a) 19 

(b) 20 

(c) 21

(d) 22

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Answer : (c) 21

. (1 + 2x + 3x2 + .....)3/2 = ((1 – x)–2)3/2 = (1 – x)–3 

∴ Coefficient of x5 = \(\frac{3.4.5.6.7}{5!}\) 

= 21

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