The 13 th term in the expansion of ( x 2 + 2 x ) n is independent of x , then the sum of the divisors of n is

Question

The $13^{th}$ term in the expansion of ${(x^{2} + \frac{2}{x})}^{n}$ is independent of $x$ , then the sum of the divisors of $n$ is

Smart Achievers · Accepted Answer

(1)

$T_{13} = {}^{n}C_{12} {(x^{2})}^{n - 12} \cdot {(\frac{2}{x})}^{12}$

$\Rightarrow x^{2 n - 24 - 12} = x^{0} \Rightarrow n = 18$

$∴$ $The sum of the divisors of n is 39$

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