Question

Find the term independent of $x$ in the expansion of
${(x^3+\frac{3}{x^3})}^{15}$

Answer 1

We have,

${(x^3+\frac{3}{x^3})}^{15}$

Therefore, $r^{th}$ term

$T_{r+1}{=}^{15}{C}_r\times (x^3{)}^r{\left(\frac{3}{x^3}\right)}^{15-r}$,

$T_{r+1}{=}^{15}{C}_r\times \left(x^{6r-45}\right)\times 3$

Here the power of $x$ term should be $0$,

$6r-45=0$

$6r=45$

$r=\frac{15}{2}$

The term independent of $x$ will be $\frac{17}{2}th$ term.

Hence, this is the answer.