If in the expansion of `(1-x)^(2n-1)` `a_r`denotes the coefficient of `x^r` then prove that `a_(r-1) +a_(2n-r)=0`

Explanation

`a_(r-1)` means coefficient of `x^{r-1}` hence term will be `T_r` and `t_r=\ ^{m-1} C_{r-1}(-x)^{r-1}`


=(-1)^{x-1}\ ^{2 m-1} C_{x-1} x^{r-1}


and `a_{2 n-r}` means coefficient corth of `x^{2 x-x}`, hence term will be `T_{2 n x+1}`


therefore T_{2 n-r+1} &=C_{2 n-r}(-X)^{2 n-r}

=(-1)^{2 n-1} C_{2 n-1} C_{2 n-r} x^{2 n-r}
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