If in the expansion of $(1+\text{x})^{20},$ the coefficients of rth and (r + 4) terms are equal, then r is equal to:

Question

Aicharya · Accepted Answer

Solution: Coefficients of the rth and (r + 4)th terms in the given expansion are ${^\text{20}}\text{C}_{\text{r}-1}$ and ${^\text{20}}\text{C}_{\text{r}}.$ Here, ${^\text{20}}\text{C}_{\text{r}-1}={^\text{20}}\text{C}_{\text{r}+3}$ $\Rightarrow \text{r}-1+\text{r}+3=20$ $\Rightarrow \text{r}=2$ or $2\text{r}=18$ $\Rightarrow \text{r}=9$

If in the expansion of \((1+\text{x})^{20},\) the coefficients of rth and (r + 4) terms are equal, then r is…

Solution