Question

Find the term independent of x in ${(x+\frac{1}{x})}^4$

Answer 1

Let $T_{r+1}$ be the term independent of x in the given expansion.
$\therefore T_{r+1}{=}^4{C}_r{x}^{4-r}{\left(\frac{1}{x}\right)}^r{=}^4{C}_r\frac{x^{4-r}}{x^r}{=}^4{C}_r{x}^{4-2r}$
For the term independent of x the power of x ,should be zero.
$\therefore 4-2r=0⟹r=2$
$⟹T_{2+1}=T_3$, is the independent term of the expansion.