1.
If a=∑n=0∞xna = \displaystyle\sum_{n=0}^{\infty} x^n, b=∑n=0∞ynb = \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