Does Splitting Non-Convergent Series Help in Proving Convergence?

[porroadventum]

1. Does the series from n=1 to ∞ of (1/2+(-1)ⁿ)/n converge?



2. Am I able to split up the series into Ʃ1/2n + Ʃ(-1)ⁿ/n even though they are not convergent? I'm not sure how else to prove for convergence. I have tried all the tests...

 

[SammyS]

1. Does the series from n=1 to ∞ of (1/2+(-1)ⁿ)/n converge?

2. Am I able to split up the series into Ʃ1/2n + Ʃ(-1)ⁿ/n even though they are not convergent? I'm not sure how else to prove for convergence. I have tried all the tests...

One of those is convergent. The other is not. So, splitting them up does help.

 

[hedipaldi]

Attached.

 

[porroadventum]

Thank you very much for the help. Much appreciated