Geometric Progression If  $S_1$, $S_2$ and $S$ are the sums of $n$ terms, $2n$ terms and to infinity of a G.P. Then, find the value of $S_1(S_1-S)$.
PS: Nothing is given about the common ratio.

HINT $\quad\:$  In $\rm\  \ (1-X)\ (1-(1-X))\ =\ 1-X^2-(1-X)\ \ \ $ put $\rm\ \ \ X = x^n\ $
then multiply both sides by $\rm\  1/(1-x)^2\ =\ S/(1-x)\:.\ \ $  More generally one has
$\rm\ \ (1-x^a)\:(1-x^b)\ =\ (1-x^a) + (1-x^b) - (1-x^{a+b})$
$\rm\quad\quad\quad\ \Rightarrow\quad\quad S_a\ S_b\ =\ S\ (S_a + S_b - S_{a+b})\:,\quad S_n = \displaystyle\frac{1-x^n}{1-x},\quad S = S_\infty = \frac{1}{1-x}$
This generalizes to arbitrary products $\rm\: S_{a}\: S_b\: S_c\cdots S_k\:$ using the Inclusion–exclusion principle.
