Find the 16th term in the expansion of

To find: $16^{\text {th }}$ term in the expansion of $(\sqrt{x}-\sqrt{y})^{17}$

Formula used: (i) ${ }^{n} C_{r}=\frac{n !}{(n-r) !(r) !}$

(ii) $T_{r+1}={ }^{n} C_{r} a^{n-r} b^{r}$

For $16^{\text {th }}$ term, $r+1=16$

$\Rightarrow \mathrm{r}=15$

$\ln ,(\sqrt{x}-\sqrt{y})^{17}$

$16^{\text {th }}$ term $=\mathrm{T}_{15+1}$

$\Rightarrow{ }^{17} C_{15}(\sqrt{x})^{17-15}(-\sqrt{y})^{15}$

$\Rightarrow \frac{17 !}{15 !(17-15) !}(\sqrt{x})^{2}(-\sqrt{y})^{15}$

$\Rightarrow 136(x)(-y)^{\frac{15}{2}}$

$\Rightarrow-136 x y \frac{15}{2}$

Ans) $-136 y \frac{15}{2}$