Question

Find the ${14}^{th}$ term from the end in the expansion of $(\sqrt{x}-\sqrt{y}{)}^{17}$.

Answer 1

${14}^{th}termin(\sqrt{x}-\sqrt{y}{)}^{17}$ from end means $5^{th}$term from starting.

$n^{th}$term from starting $=\left(\begin{array}{c}17\\ n-1\end{array}\right)\left(\sqrt{x}{)}^{18-n}\right(\sqrt{y}{)}^{n-1}.(-1{)}^{n-1}$

$=\left(\begin{array}{c}17\\ n-1\end{array}\right).x^{\frac{13}{2}}.y^2$