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Home » Prove that the coefficient of (r + 1)th term in the expansion of (1 + x)n + 1 is equal to the sum of the coefficients of rth and (r + 1)th terms in the expansion of (1 + x)n.
Prove that the coefficient of (r + 1)th term in the expansion of (1 + x)n + 1 is equal to the sum of the coefficients of rth and (r + 1)th terms in the expansion of (1 + x)n.
Binomial Theorem | CBSE | Class 11 | Exercise 18.2 | Maths | RD Sharma
Prove that the coefficient of (r + 1)th term in the expansion of (1 + x)n + 1 is equal to the sum of the coefficients of rth and (r + 1)th terms in the expansion of (1 + x)n.

Answer:

Given,

Coefficients of (r + 1)th term in (1 + x)n+1 =  n+1Cr

Sum of the coefficients of the rth and (r + 1)th terms in (1 + x)n ,

(1 + x)n = nCr-1 + nCr

= n+1Cr [since, nCr+1 + nCr = n+1Cr+1]

Thus, proved.

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