Mathematics - Binomial Theorem Question with Solution | TestHub

If $a_1={}^n{C}_r$ then $\frac{a_1}{a_1+a_2}=\frac{{}^n{C}_r}{{}^n{C}_r+{}^n{C}_{r+1}}=\frac{1}{1+\frac{n-r}{r+1}}=\frac{r+1}{n+1}$ Similarly $\frac{a_2}{a_2+a_3}=\frac{r+2}{n+1}$ and $\frac{a_3}{a_3+a_4}=\frac{r+3}{n+1}$ $\frac{r+1}{n+1},\frac{r+2}{n+1},\frac{r+3}{n+1}$ are in A.P.