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If (1 + x) n = C0 + C1x + C2x2 + .... + Cnxn, then C0 + 3 . C1 + 5 . C2 + .... + (2n + 1) . Cn equals

(a) 22n–1 

(b) (n + 1) 2n 

(c) n . 2n+1 

(d) (n – 1) 2n–1

1 Answer

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Best answer

Answer : (b) (n + 1) 2n 

C0 + 3C1 + 5C2 + ..... (2n + 1) Cn 

= (C0 + C1 + C2 + ..... + Cn) + (2C1 + 4C2 + ..... + 2n Cn

= 2n + 2 (C1 + 2C2 + 3.C3 + ..... + n Cn

= 2n + 2 × n . 2n–1 

 = 2n + n . 2n 

= 2n (n + 1).

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