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Prove that the term independent of x in ...

Prove that the term independent of `x` in the expansion of `(x+1/x)^(2n) \ is \ (1. 3. 5 ... (2n-1))/(n !). 2^n`.

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Given
`(x+frac{1}{x})^{2 n}`
Suppose the term independent of `x` is the `(r+1)` th term .
`therefore T_{r+1}=\ ^{2 n} C_{r} x^{2 n-r} frac{1}{x^{r}} `
...
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