Re: Does the series 1 - 1/2 - 1/3 + 1/4 + 1/5 - 1/6 - 1/7 + 1/8 + 1/9 + ... converges?


"A N Niel" <anniel@xxxxxxxxxxxxxxxxxxxxx> wrote in message
news:030420051512053050%anniel@xxxxxxxxxxxxxxxxxxxxxxxx
> In article <882ebff2.0504030724.14392f8f@xxxxxxxxxxxxxxxxxx>, dalthman
> <dalthman@xxxxxxxxxxx> wrote:
>
>> Does the series 1 - 1/2 - 1/3 + 1/4 + 1/5 - 1/6 - 1/7 + 1/8 + 1/9 + ...
>> converges?
>>
>> And also how can we know whether such kind of series converge or not?
>
> Yes, the absolute values 1, 1/2, 1/3, ... decrease to zero,
> and the sign series 1-1-1+1+1... has bounded partial sums.

I think this is the best method. Something about regrouping the terms of a
conditionally convergent series makes me nervous.


.

Quantcast