The sum of all rational terms in the expansion of \left(2^{\frac{1}{5}}+5^{\frac{1}{3}}\right)^{15} is equal to :

Question

Accepted Answer

Answer: C. 3133 \begin{aligned} & T_{r+1}={ }^{15} \mathrm{C}_r\left(2^{1 / 5}ight)^{15-r}\left(5^{1 / 3}ight)^r \ & ={ }^{15} C_r 5^{r / 3} 2^{\left(3-\frac{r}{5}ight)} \end{aligned} For rational terms, \frac{r}{3} and \frac{r}{5} must be integer 3 and 5 divide r \Rightarrow 15 divides r \Rightarrow r=0 and r=15 { }^{15} C_0 5^0 2^3+{ }^{15} C_{15} 5^5 2^{(0)} \begin{aligned} & =8+3125 \ & =3133 \end{aligned}

The sum of all rational terms in the expansion of $$\left(2^{\frac{1}{5}}+5^{\frac{1}{3}}\right)^{15}$$ is equal to :

Answer

Explanation

More JEE Math questions