1. ## Infinite Series

I have no idea how to do this. Any help????

Consider an infinite series of the form

± 3 ± 1 ± 1/3 ± 1/9 ± 1/27 ± · · · ± 1/(3^n) ± · · ·

The numbers 3, 1, etc., are given but you will decide what the signs should be.

a) Can you choose the signs to make the series diverge?
b) Can you choose the signs to make the series sum to 3.5?
c) Can you choose the signs to make the series sum to 2.25?

*They all might not be possible....

Could someone explain how these are done.

2. Originally Posted by TreeMoney
a) Can you choose the signs to make the series diverge?
It is not possible to make the series diverge. No matter what signs you choose, the series converges absolutely. Hence the series converges.

Originally Posted by TreeMoney
b) Can you choose the signs to make the series sum to 3.5?
Change all signs to negative, except for the signs in front of 3 and 1, which remain positive.