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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.

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To solve the problem, we need to find the value of \( n \) such that the expansion of \( (x - \frac{1}{x^2})^{2n} \) contains a term independent of \( x \). ### Step-by-Step Solution: 1. **Identify the Binomial Expansion**: The expression can be expanded using the Binomial Theorem: \[ (a + b)^n = \sum_{r=0}^{n} \binom{n}{r} a^{n-r} b^r ...
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