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If (1 + x) ^n = C0 + C1x + C2x^2 + .... + Cnx^n, then the sum C1 + 2 . C2 + 3 . C3 + .... + n . Cn equals

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If (1 + x)n = C0 + C1x + C2x2 + .... + Cnxn, then the sum C1 + 2 . C2 + 3 . C3 + .... + n . Cn equals

(a) 2n–1 

(b) (n – 1) 2n–1 

(c) n . 2n–1 

(d) (n – 1) 2n

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Answer : (c) n . 2n–1 

(1 + x)n = nC0 + nC1 x + nC2 x2 + .... + nCn xn 

= C0 + C1x + C2 x2 + ..... + Cn xn 

∴ C1 + 2.C2 + 3.C3 + ..... + n.Cn

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