If the coefficients of `a^(r-1),\ a^r and \ a^(r+1)` in the binomial expansion of `(1+a)^n` are in A.P., prove that `n^2-n(4r+1)+4r^2-2=0.`

Explanation

coefficient of `a r^{-1}` in `(1+a)^{{n}}`


`\ ^{n} C_{r-1}(1)^{n-r+1}(a)^{r-1} `


`a^{r}=\ ^{n} C_{r}(1)^{{n}-{r}}(a)^{{r}}`


Factors `a^{{r}+1}+^{{n}} {C}_{{r}+1}(1)^{{n}-{r}-1} {a}^{{r}+1}`


...