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in Mathematics by (53.3k points)

If C0 , C1 , C2 , ...................Cn are the binomial coefficients in expansion of (1 + x)n , n being even, then C0 + (C0 + C1) + (C0 + C1 + C2) +..........+ (C0 + C1 +......+Cn–1) is equal to

(a)   n.2n 

(b)  n.2n–1 

(c)   n.2n–2 

(d)  n.2n–3 

1 Answer

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Best answer

Correct option  (b) n.2n–1

Explanation:

∴ C0 + (C0 + C1 ) +.........+ (C0 + C1 +.......Cn–2) + (C0 + C1 +..........Cn–1)

= (Cn) + (Cn + Cn–1) +.......+ (C0 + C1 +.........+ Cn–2) + (C0 + C1 +.....+ Cn–1)

= 2+ 2+ 2+... n/2 times (Adding the terms equidistant from the begining and the end)

= n/2 . 2n = n.2n–1

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