Can Two Divergent Series Multiply to a Convergent Series?

[Denisse]

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

 

[micromass]

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

 

[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)?