# diverging sequences - sum/product converging

• Jan 11th 2010, 12:58 PM
ozfingwe
diverging sequences - sum/product converging
hello,

I am supposed to find two diverging sequences whose sum and products converge, and whose elements are all >= 0. Anyone who could give me a hint? (-1)^n and (-1)^(n+1) works execpt for that fact that not all elements are >= 0.

thank you -
oz.
• Jan 11th 2010, 01:01 PM
Drexel28
Quote:

Originally Posted by ozfingwe
hello,

I am supposed to find two diverging sequences whose sum and products converge, and whose elements are all >= 0. Anyone who could give me a hint? (-1)^n and (-1)^(n+1) works execpt for that fact that not all elements are >= 0.

thank you -
oz.

I am not sure if this is what you mean. You should be more specific.

$\displaystyle a_n=-n,\tilde{a}_n=n+1,a_n+\tilde{a}_n=1$

$\displaystyle b_n=(-1)^n,\tilde{b}_n=(-1)^n$
• Jan 11th 2010, 01:10 PM
ozfingwe
I'm sorry for the confusion, the sequences must hold to this:

an >= 0 and bn >= 0 for all n...

oz.