username2207531
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"Find the value of the term in the expansion of (x-(1/x))^8 which is independent of x."

I've been using the nCr function and it worked great so far, but I'm not sure how to do this question since both values in the brackets have x in them.

Thanks in advance.
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Zacken
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(Original post by JustJusty)
"Find the value of the term in the expansion of (x-(1/x))^8 which is independent of x."

I've been using the nCr function and it worked great so far, but I'm not sure how to do this question since both values in the brackets have x in them.

Thanks in advance.
The rth term of this expansion is going to be \displaystyle {8 \choose r} x^{8-r}\ \cdot \left(-\frac{1}{x}\right)^r = {8 \choose r}x^{8-r} \cdot (-1)^r \cdot x^{-r} = {8 \choose r} x^{8-r-r} (-1)^r

So this term will be independent of x when the exponent of x becomes 0. For what value of r is this?
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