IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

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find the sum of the series :

1².ⁿc₁+3².ⁿc₃+5².ⁿc₅+-------------------upto n terms

(A) n(n-1)2^n-2+n2^n-1 (B) n²2^n-2

(C) n(n-1)2^n-3 (D) n(n-1)2^n-3+n.2^n-2

pls also explain ur answer

iitkgp_bipin

The most effective way of solving this objective question would be put n=1.

Then sum of series = (1²)(¹C₁) = 1

For n=1

A) 1 , B) 1/2 , C) 0 , D)1/2

Hence correct option is A).

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