General formula for the power series of $\dfrac{1}{(1+x)^3}$ I wish to find the general formula for the following power series:
$\dfrac{1}{(1+x)^3}=1-3x+6x^2-10x^3+15x^4-21x^5+28x^6...$
The difference between the first and second term is $2$
The difference between the second and third term is $3$
The difference between the third and fourth term is $4$
The difference between the fourth and fifth term is $5$
and so on.
How do you find the general formula for this series? It is not quite an arithmetic series, and definitely not a geometric series, so what should I do?

$$\frac {1}{1+x} = 1-x+x^2-x^3+x^4-....$$
Differentiate and you get 
$$ \frac {-1}{(1+x)^2} = -1+2x-3x^2+4x^3-....$$
Differentiate again and you get 
$$ \frac {2}{(1+x)^3} = 2-6x+12x^2-....$$
$$ \frac {1}{(1+x)^3} = 1-3x+6x^2-....$$ 
