Hello, i am unsure how to do this question... Find the value of the term in the expansion of (1-1/x)^8 which is independent of x. How do i do this? I have no problem with normal expansions but how do you do one with a fraction in?
Thankyou,
Kris.
Hello, i am unsure how to do this question... Find the value of the term in the expansion of (1-1/x)^8 which is independent of x. How do i do this? I have no problem with normal expansions but how do you do one with a fraction in?
Thankyou,
Kris.
I assume independent of x means it has no x term and is just a constant.
Then it's a matter of observation. It's 1. Becasue of the 1 in $\displaystyle (1-\frac{1}{x})^{8}$
If you have $\displaystyle (p+q)^{8}$, just sub in -1/x where the q goes in the expansion. Fractions are no different than an integer.
$\displaystyle 1^{8}+8(\frac{-1}{x})+28(\frac{-1}{x})^{2}+...........+(\frac{-1}{x})^{8}$
I suspect there is a typo in your original post: you probably want the constant term in the expansion of $\displaystyle \left(\color{red}x\color{black}-\frac{1}{x}\right)^8$. This would be the term $\displaystyle ^8\mathrm{C}_4\,x^4\,\left(-\frac{1}{x}\right)^4$.