How Do Telescoping Sums Relate to Squares in Mathematical Proofs?

[nameVoid]

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

 

[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.

 

[Count Iblis]

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

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.