# Homework Help: Proof help

1. Oct 21, 2008

### lalalalizzay

How do you prove ex * ey = ex + y using series?

Prove:

suppose sum an and sum bn converge absolutely then the series cn with cn = sum (from k=0 to n) ak*bn-k converges absolutely to the limit sum an * sum bn

Thank you!

Or if you have seen either of these on here could you redirect me to that page

2. Oct 22, 2008

### Tac-Tics

For the first one, what is the formula for e^x? That should make the proof obvious.

For the second one, I don't know, and dinner's ready, but it probably follows from using the epsilon-delta definition of a limit.

3. Oct 22, 2008

### Dick

Hint: (a0+a1)*(b0+b1)=a0*b0 + (a0*b1+a1*b0) + a1*b1. In the first term the indices sum to 0, in the second to 1 and in the last to 2. Do you see how that is related to what you are asking?