Question

what is the middle term of the following exansion and is there a fast way to do it other than just expanding the entire thing?

(x - 1/x)^6

Answer 1

hi
i did some help

Answer 2

You can use Pascal's triangle to solve this quickly. It goes:
\[
\begin{align*}
&1\\
1\quad & \qquad 1\\
1\qquad &2\qquad 1\\
1 \qquad 3 &\quad 3 \qquad 1\\
&....
\end{align*}
\]
This lets you solve the problem more quickly. If you have an expansion \((a+b)^n\), you can look at the \((n+1)\) row of the triangle and use the numbers in it to find the coefficients of the expansion:
\[
\begin{align*}
&(a+b)^2\\
&\Rightarrow a^2 + 2ab + b
\end{align*}
\]
Note that \(n=2\) and the third rows numbers were [1 2 1], which appeared as coefficients here. The seventh row is [1 6 15 20 15 6 1]. Can you solve your problem from that?

Answer 3

OR
http://www.wolframalpha.com/input/?i=(x+-+1%2Fx)^6

Answer 4

hi
can i attach file

Answer 5

Include the ^6 in the last link

Answer 6

interesting, i'll definitely have to look at pascal's triangle more closely, much easier than expanding.

Answer 7

Yep, it's pretty awesome.

Answer 8

thank you very much!

Answer 9

yay