# A problem

1. Nov 7, 2004

### 3.14lwy

if
Xn = x^n + x^(n-2) + x^(n-4) + ... + 1/[x^(n-4)] + 1/[x^(n-2)] + 1/(x^n)
(where n is a non-negative integer)

then ,

X1 = x + 1/x

X3 = x^3 + x + 1/x + 1/(x^3)

What s the value of X2??

X2 = x^2 + x^0 + 1/(x^2) = x^2 + 1 + 1/(x^2)

or X2 = x^2 + x^0 + 1/(x^0) + 1/(x^2) = x^2 + 1 + 1 + 1/(x^2)
????

2. Nov 7, 2004

### Zurtex

In your definition you decreased the power of x by 2 each time, so:

$$x2 = x^2 + x^0 + x^{-2} = x^2 + 1 + \frac{1}{x^2}$$

For $x \neq 0$