1.
If a=n=0xna = \displaystyle\sum_{n=0}^{\infty} x^n, b=n=0ynb = \displaystyle\sum_{n=0}^{\infty} y^n, c=n=0(xy)nc = \displaystyle\sum_{n=0}^{\infty} (xy)^n where x,y<1|x|, |y| < 1, then