The sum of all those terms which are rational numbers in the
expansion of (21/3 + 31/4)12 is :
Solution
$${T_{r + 1}} = {}^{12}{C_r}{\left( {{2^{1/3}}} \right)^r}.{\left( {{3^{1/4}}} \right)^{12 - 4}}$$<br><br>T<sub>r + 1</sub> will be rational number when r = 0, 3, 6, 9, 12 & r = 0, 4, 8, 12<br><br>$\Rightarrow$ r = 0, 12<br><br>T<sub>1</sub> + T<sub>13</sub> = 1 $\times$ 3<sup>3</sup> + 1 $\times$ 2<sup>4</sup> $\times$ 1<br><br>= 24 + 16 = 43
About this question
Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion
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