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+1 vote
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in Mathematics by (71.2k points)
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(1+x)n = nC0 + nC1 x +nC2 x2 +----- nCnxn . and nC1/nC0 + 2nC2/nC1 +  3 nC3/nC2 + .......+ nCn/nC-1 = 1/k n(n+1) then K = ______

(a) 3 

(b) 6 

(c) 2 

(d) 12

1 Answer

+1 vote
by (76.3k points)
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Best answer

Correct option: (c) 2

Explanation:

we know [(nCr) / (nCr–1)] = [(n – r + 1) / r]

givennr=1 r ∙ [(nCr) / (nCr–1)]

nr=1 (n – r + 1)

nr=1 (n + 1 – r)

= (n + r – 1) + (n + 1 – 2) (n + 1 – 3) + ------- (n + 1 – n)

= n + (n – 1) + (n – 2) + ----- 1

= sum of terms in A. P.

= (n/2)(1 + n) = (n/2)(n + 1)

  k = 2

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