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Binomial Theorem Part 3

Section: Mathematics

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Question : 51 of 53

Marks: +1, -0

The sum of all rational terms in the expansion of

\left(2^{\frac{1}{5}} + 5^{\frac{1}{3}}\right)^{15}

[4 Apr 2024 Shift 1]

3133
633
931
6131

Solution: 👈: Video Solution

\; T_{r+1} = {}^{15}C_{r} \left(5^{\frac{1}{3}}\right)^{r} \left(2^{\frac{1}{5}}\right)^{15-r}

\; = {}^{15}C_{r} 5^{\frac{r}{3}} \cdot 2^{\frac{15-r}{5}}

\; R = 3\lambda, 15\mu

\; \Rightarrow r = 0, 15

\; 2 \; \text{rational terms} \;

\; \Rightarrow {}^{15}C_0 2^3 + {}^{15}C_{15} (5)^5

\; = 8 + 3125 = 3133

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