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The 13^(th) term in the expanion of (x^(...

The `13^(th)` term in the expanion of `(x^(2)+2//x)^(n)` is independent of `x` then the sum of the divisiors of `n` is

A

`36`

B

`37`

C

`38`

D

`51`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `13^(th)` term in expansion `(x^(2)//2x)^(n)` is
`.^(n)C_(12)(x^(2))^(n-12)(2//x)^(12)=^(n)C_(12)x^(2n-36)`
Given `13^(th)` term is independent of `x`
`:.n=18`
`:. ` Divisors of `18` are `1,2,3,6,9,12,18` sum of which is `51`
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