how that the coefficient of (r+1) th in the expansion of `(1+x)^(n+1)` is equal to the sum of the coefficients of the r th and (r+1) th term in the expansion of `(1+x)^n`

Explanation

Coefficient of the `(\{r}+1)` th term in `(1+x)^{n+1}` is `\ ^{n+1} C_{r}`

Sum of the coefficients of the rth and `(r+1)` th terms in `(1+x)^{n}=\ ^{n} C_{r-1}+\ ^{n} C_{r}`

`=\ ^{n+1} C_{r}` `[\ ^{n} C_{r+1}+\ ^{n} C_{r}=\ ^{n+1} C_{r+1}\]`

Hence proved.