The sum of all rational terms in the expansio | vedclass

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Question

$ \mathrm{T}_{\mathrm{r}+1}={ }^{15} \mathrm{C}_{\mathrm{r}}\left(5^{\frac{1}{3}}\right)^{\mathrm{r}}\left(2^{\frac{1}{5}}\right)^{15-\mathrm{r}} $

Vedclass · Accepted Answer

$3133$

Vedclass · Answer

$ \mathrm{T}_{\mathrm{r}+1}={ }^{15} \mathrm{C}_{\mathrm{r}}\left(5^{\frac{1}{3}}ight)^{\mathrm{r}}\left(2^{\frac{1}{5}}ight)^{15-\mathrm{r}} $

$ ={ }^{15} \mathrm{C}_{\mathrm{r}} 5^{\frac{\mathrm{r}}{3}} \cdot 2^{\frac{15-\mathrm{r}}{5}} $

$ \mathrm{R}=3 \lambda, 15 \mu $

$ \Rightarrow \mathrm{r}=0,15 $

$ 2 	ext { rational terms } $

$ \Rightarrow{ }^{15} \mathrm{C}_0 2^3+{ }^{15} \mathrm{C}_{15}(5)^5 $

$ =8+3125=3133$

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

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