Are the sum and/or product of two divergent sequences divergent?

As a counterexample -- while looking for two divergent sequences whose sum or product converges we have the obvious choice, (1, -1, 1, -1, . . . ) with (-1, 1, -1, 1 . . . ) but is there another cool example of this?

Re: Are the sum and/or product of two divergent sequences divergent?

Quote:

Originally Posted by

**CountingPenguins** As a counterexample -- while looking for two divergent sequences whose sum or product converges we have the obvious choice, (1, -1, 1, -1, . . . ) with (-1, 1, -1, 1 . . . ) but is there another cool example of this?

Re: Are the sum and/or product of two divergent sequences divergent?

Quote:

Originally Posted by

**CountingPenguins** As a counterexample -- while looking for two divergent sequences whose sum or product converges we have the obvious choice, (1, -1, 1, -1, . . . ) with (-1, 1, -1, 1 . . . ) but is there another cool example of this?

EDIT: Oooops... you asked for sequences and I give you a series...(But it can work as well)

is converges.

But, isn't.

Re: Are the sum and/or product of two divergent sequences divergent?

Edit: disregard this. The left forum sidebar protruded over the formula for and obscured the minus.

Quote:

Originally Posted by

**Also sprach Zarathustra**

Isn't the harmonic series? Then it does not converge.

Re: Are the sum and/or product of two divergent sequences divergent?

Quote:

Originally Posted by

**emakarov** Edit: disregard this. The left forum sidebar protruded over the formula for

and obscured the minus.

Isn't

the harmonic series? Then it does not converge.

Actually I forgot '1' in the sum S_1... (I'll fix it in my post)