Question

Question on power series.

Answer 1

Why does \[\sum_{n=2}^{\infty}\frac{ n(n-1) }{ 2 }x^n = \sum_{n=1}^{\infty}\frac{ n(n-1) }{ 2 }x^n\]the index changed from n = 2 to n =1, yet the power series did not change at all?

Answer 2

Hint :
x = 0 + x

Answer 3

Is it because when you plug in n = 1, you get 0, so if we changed the starting summation from n=2 to n=1, it wouldn't make a difference at all since it won't make an impact?

Answer 4

Exactly!