Term independent of \(x\) in \((a/x+bx)^n\) for JEE

Formula

\[\text{Constant term exists when }2r-n=0\;\Rightarrow\; r=\frac{n}{2},\quad T_{\frac{n}{2}+1}={n\choose \frac{n}{2}}a^{\frac{n}{2}}b^{\frac{n}{2}}\]

Variables: \(n\) is a positive integer.

Conditions: Exists only when \(n\) is even.

Very common constant-term question.