What is the Closed Form of the Power Series 1+3x+6x^2+10x^3+15x^4+21x^5+...?

[trains99]

Homework Statement

Find the closed form of the following power series
1+3x+6x^2+10x^3+15x^4+21x^5+...

Homework Equations

1+x+x^2+.. = 1/(1-x)

The Attempt at a Solution

I tried differentiating but couldn't get it to any expression that I know the sum for.. I was playing around trying to find some kind of increasing arithmetic sum but couldn't figure out how to get the closed form

 

[Dick]

Take 1+x+x^2+... = 1/(1-x) and differentiate both sides. Now do it again. Are you seeing anything useful in the second derivative?

 

[trains99]

Great, got it thanks:)