Convergent and divergent series

1. Apr 20, 2013

Denisse

Is it posible that the product of two different divergent series be a convergent serie?

2. Apr 21, 2013

micromass

Staff Emeritus
Take $x_n = 1/n$ and $y_n = (-1)^n$.

3. Apr 21, 2013

chiro

Hey Denisse and welcdme to the forums.

Do you mean like an inner product (i.e. z_n = x_n * y_n) or do you mean you multiply two whole final values together? (Like z = x * y where x is final value for series x and similar for y_n)?