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

Explanation

Coefficients of the pth and q th terms are `\ ^{n} C_{p-1}` and `\ ^{n} C_{q-1}` respectively .


Thus, we have:


`\ ^{n} C_{p-1}=\ ^{n} C_{q-1} `


`Rightarrow p-1=q-1 { or } p-1+q-1=n[: cdot\ ^{n} C_{r}=\ ^{n} C_{s}Rightarrow r=s or, r+s=n] `


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