Question

In the expansion of ${(x+\frac{2}{x^2})}^{15}$, the term independent of x is

• A. ${}^{15}{C}_6{2}^6$
• B. ${}^{15}{C}_5{2}^5$
• C. ${}^{15}{C}_4{2}^4$
• D. ${}^{15}{C}_8{2}^8$

Answer 1

The correct option is B ${}^{15}{C}_5{2}^5$

$(15-r)\left(1\right)+r(-2)=0\Rightarrow 15-3r=0\Rightarrow r=5$
Thus term independent of x is
${=}^{15}{C}_5\left(1{)}^{10}\right(2{)}^5{=}^{15}{C}_5{2}^5$.