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+1 vote
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in Binomial Theorem by (53.3k points)
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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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by (53.5k points)
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Best answer

Correct option is (b) n.2n–1

\(\therefore\) C0 + (C0 + C1)+.........+ (C0 + C1 +.......Cn–2) + (C0 + C1 +..........Cn–1)

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

= 2n + 2n + 2n +...\(\frac n2\)times (Adding the terms equidistant from the begining and the end)

\(= \frac n2 .2^n = n.2^{n-1}\)

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