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Question

If in the expansion of (1 + x)n, the coefficients of pth and qth terms are equal, prove that p + q = n + 2, where pq.


Solution

Coefficients of the pth and qth terms are Cp-1n and Cq-1n respectively.Thus, we have:Cp-1n= Cq-1np-1 =q-1 or, p-1+q-1=n             [ Crn=nCsr=s or, r+s=n]p=q or, p+q=n+2

If pq, then p+q=n+2
Hence proved

Mathematics
RD Sharma XI (2015)
Standard XI

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