converge of series

[fjalhada]

is this series converge or diverge

i need the proved

 

[fjalhada]

I put this proof but I'm not sure

is diverge

 

[blamocur]

I put this proof but I'm not sure
View attachment 31497
is diverge

I must be missing something since I don't see a proof here. What is [imath]v_n[/imath]? And why using [imath]\cos(n\pi)[/imath] is better than using [imath](-1)^n[/imath] ?

 

[Steven G]

That last line means nothing since v_n is not the summand.

 

[fjalhada]

That last line means nothing since v_n is not the summand.

and this series convege?

 

[lookagain]

and this series convege?
View attachment 31528

fjalhada, do not post this problem here. Instead, post this problem in a new thread for discussion.

 

[Deleted member 4993]

fjalhada, do not post this problem here. Instead, post this problem in a new thread for discussion.

I think s/he was referring to discussion of OP (refer post #2) - which is:

 

[BigBeachBanana]

and this series convege?
View attachment 31528

I would apply the root test to determine the convergence of the series, but I haven't worked it out yet.

 

[lookagain]

I think s/he was referring to discussion of OP (refer post #2) - which is:

View attachment 31538

I don't see the series given in post #5 in any of the steps in post #2 of the OP.