The sum of the rational terms in the binomial expansion of…
The sum of the rational terms in the binomial expansion of $\left(2^{\frac{1}{2}}+3^{\frac{1}{5}}\right)^{10}$ is :
25
32
9
41
Solution
$\left(2^{1 / 2}+3^{1 / 5}\right)^{10}={ }^{10} \mathrm{C}_0\left(2^{1 / 2}\right)^{10}$
$
+{ }^{10} \mathrm{C}_1\left(2^{1 / 2}\right)^9\left(3^{1 / 5}\right)+\ldots \ldots+{ }^{10} \mathrm{C}_{10}\left(3^{1 / 5}\right)^{10}
$
There are only two rational terms - first term
and last term.
Now sum of two rational terms
$
=(2)^5+(3)^2=32+9=41
$