The Total solution for NCERT class 6-12
Prove that the coefficient of (r + 1)th term in the expansion of (1+ x)n + 1 is equal to the sum of the coefficientsof rth and (r + 1)th terms in the expansion of (1 + x)n.
We know, thecoefficients of (r + 1)th term in (1 + x)n+1 is n+1Cr
So, sum of thecoefficients of the rth and (r + 1)th terms in (1 + x)n is
(1 + x)n = nCr-1 + nCr
= n+1Cr [since, nCr+1 + nCr = n+1Cr+1]
Hence proved.