Binomial Theorem

Hi Heureka, 

Chris and I were discussing just this morning that we wished you would come back.

Were your ears burning?

It is really GREAT to see you again  :)

Why there are 2 of the same post help LOL

What's

$(x+\frac{1}{x})^4 ~ \text{ ?}$

$\begin{array}{rcll} && (x+\frac{1}{x})^4\\ &=& \binom40 \cdot x^4 + \binom41 \cdot x^3 \cdot \frac1x + \binom42 \cdot x^2 \cdot \frac1{x^2} + \binom43 \cdot x \cdot \frac1{x^3} + \binom44 \cdot \frac1{x^4} \\ &=& 1 \cdot x^4 + 4 \cdot x^3 \cdot \frac1x + 6 \cdot x^2 \cdot \frac1{x^2} + 4 \cdot x \cdot \frac1{x^3} + 1 \cdot \frac1{x^4} \\ &=& x^4 + 4 \cdot x^2 + 6 + \frac4{x^2} + \frac1{x^4} \\ \end{array}$

x=i, -i