Evaluate : C 0 2 + + +…..+

Maths Binomial Theorem & Mathematical Induction Mix Subjective Type

Published on: August 12, 2026

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Sol. Given (1+ x) n = C 0 + C 1 x +…..+ C n x n

Integrating both sides w.r.t. x from 0 to x.

So, = C 0 x + + +…..+

...(1)

and (x + 1) n = C 0 x n + C 1 x n–1 +…..+C n …(2)

Multiplying (1) and (2), we get

{(1+ x) 2n+1 – (1+ x) n }

= . (C 0 x n + C 1 x n–1 +…..+ C n )

Now equate coefficient of x n+1 on both sides

⇒ required sum =

= 2n+1 C n+1 .

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