Proof of an infinite series formula If $$|x| < 1$$ Prove that
$$\begin{align}\large 1 + 2x + 3x^2 + 4x^3 + \dots = \frac{1}{(1 - x)^2}\end{align}$$

Another$^2$ approach:
Since
$\sum_{i=0}^{\infty} x^i
= \frac1{1-x}
$,
differentiating both sides
we get
$\sum_{i=1}^{\infty} ix^{i-1}
= \frac1{(1-x)^2}
$.
