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If the expansion of (x - (1)/(x^(2)))^(2...

If the expansion of `(x - (1)/(x^(2)))^(2n)` contains a term independent of x, then `n` is a multiple of 2.

Text Solution

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Given Binomial expansion is `(x - (1)/(x^(2)))^(2n)`
Let `T_(r + 1)` term is independent of `x`
Then, `T_(r + 1) = .^(2n)C_(r) (x)^(2n - r) (-(1)/(x^(2)))^(r)`
`= .^(2n)C_(r) x^(2n - r) (-1)^(r) x^(-2r) = .^(2n)C_(r) x^(2n - 3r) (-1)^(r)`
For independent of `x`
`2n - 3 r = 0`
`:. r = (2n)/(3)`
Which is not a integer
So, the given expansion is not possible
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