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

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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
 
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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?
 
Great, got it thanks:)
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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