Constant term in the expansion of $\Big(\text{x}-\frac{1}{\text{x}}\Big)^{10}$ is:

Question

Aicharya · Accepted Answer

Solution: Suppose (r + 1) th term is the constant term in the given expansion. Then, we have $\text{T}_{\text{r}+1}={^\text{10}}\text{C}_{\text{r}}\ \text{x}^{10-\text{r}}\ \Big(\frac{\text{1}}{\text{x}}\Big)^{\text{r}}$ $={^\text{10}}\text{C}_{\text{r}} (-1)^{\text{r}}\ \text{x}^{10-\text{r}-\text{r}}$ For this term to be constant, we must have $10-2\text{r}=0$ $\Rightarrow \text{r}=5$ Required term $={^\text{10}}\text{C}_{\text{5}}=-252$

Constant term in the expansion of \(\Big(\text{x}-\frac{1}{\text{x}}\Big)^{10}\) is:

Solution