The sum of all those terms which are rational numbers in the expansion of (21/3 + 31/4)12 …

Question

The sum of all those terms which are rational numbers in the expansion of (21/3 + 31/4)12 is :

Accepted Answer

$${T_{r + 1}} = {}^{12}{C_r}{\left( {{2^{1/3}}} \right)^r}.{\left( {{3^{1/4}}} \right)^{12 - 4}}$$

Tr + 1 will be rational number when r = 0, 3, 6, 9, 12 \& r = 0, 4, 8, 12

$$\Rightarrow$$ r = 0, 12

T1 + T13 = 1 $$\times$$ 33 + 1 $$\times$$ 24 $$\times$$ 1

= 24 + 16 = 43

Solutions · 1