The coefficient of x 4 in $\Big(\frac{\text{x}}{2}-\frac{3}{\text{x}^{2}}\Big)$ is:

Question

Aicharya · Accepted Answer

Solution: Suppose x 4 occurs at the (r + 1) th term in the given expansion. Then, we have $\text{T}_{\text{r}+1}={^\text{10}}\text{C}_{\text{r}}\Big(\frac{\text{x}}{2}\Big)^{10-\text{r}}\Big(\frac{-3}{2\text{x}^{2}}\Big)$ $=(-1)^{\text{r}}\ {^\text{10}}\text{C}_{\text{r}}\frac{3^{\text{r}}}{2^{10-\text{r}}}\text{x}^{10-\text{r}-2\text{r}}$ For this term to contain x 4 , we must have $10-3\text{r}=4$ $\Rightarrow \text{r}=2$ $\therefore$ Required coefficient $={^\text{10}}\text{C}_{\text{2}}\frac{3^{2}}{2^{8}}=\frac{10\times9\times9}{2\times2^{8}}=\frac{405}{256}$

The coefficient of x 4 in \(\Big(\frac{\text{x}}{2}-\frac{3}{\text{x}^{2}}\Big)\) is:

Solution