Need help. Im a student.
Is every serie that alternates between + and - and has a limit 0 convergent?
I cant think of one that isnt?
Then probably it is. Try to proof it.
>>8004152
Im an engineering student not maths. Not exactly sure how I would go about proofing it.
>>8004146
yes
https://en.wikipedia.org/wiki/Alternating_series_test
>>8004157
Why does it specifically say if it decreases? Is there any case where an alternating series with limit 0 that increases and not convergent?
>>8004167
Decrese in absolute value tard.
>>8004171
Well it has to decrease in absolute value if it has a limit of 0? Is there any other way?
>>8004178
Yes, a non monotonic decrease.
>>8004167
>s there any case where an alternating series with limit 0 that increases and not convergent?
are you talking about the series having a limit of zero? or the limit of the underlying sequence?
>>8004187
Okay so:
>Aternating
>monoton
>limit=0
Means convergent? No need to mention a decrease.
>>8004191
limit of underlying sequence. I dont know much maths in english thanks for correcting me on that.
>>8004199
Actually does monotonic really matter? Just these in underlying sequence:
>alternates
>limit=0
seems to be enough to ensure a convergent serie with my knowledge.
