Question

How would you determine the power series of 1/(1-x)^3. I know that the series of 1/(1-x) is x^n, but how would you manipulate it for this scenario?

Answer 1

I got 1+3x+6x^2+10x^3+15x^4... but I was wondering how I would write a series for this.

Answer 2

surely you recognize the sequence

1, 3, 6, 10, ... as n(n+1)/2

it is the sequence of partial sums of

1+2+3+4+...