# Sum of squares proof

1. May 6, 2009

### nameVoid

the proof in my text starts with whats called a telescoping sum (1+i^3)-i^3 what is the relevence of this to i^2

2. May 6, 2009

### Count Iblis

a) Prove the formula for the partial geometric series:

$$\sum_{k=0}^{n}x^{k}=\frac{1-x^{n+1}}{1-x}$$

Hint: Multiply both sides by 1-x.

b) Substitute x = e^t in the formula for the partial geometric series.

c) Perform a series expansion of both sides to second order in t.

3. May 6, 2009

### Count Iblis

Shouldn't that be (1+i)^3 - i^3?

If you expand (i+1)^3, you see that i^3 cancels and then you get a combinaton of the summaton of i^2 and i and of 1.