- #1
mscudder3
- 29
- 0
The definition I am working from is "Let Z=(z(sub n)) be a decreasing sequence of strictly positive numbers with lim(Z)=0. Then the alternating series, Sum(((-1)^n)*Z) is convergent.
My question is how to solve the following:
If the hypothesis that Z is decreasing is dropped, show the Alternating Series Test may fail.
I am aware of a proof utilizing some Z that is also alternating, but this breaks the condition that Z is strictly positive. I am unaware of an such sequence that has a limit of 0, all elements of the series are positive, yet is divergent.
This question is due within 10 hours. Please help!
My question is how to solve the following:
If the hypothesis that Z is decreasing is dropped, show the Alternating Series Test may fail.
I am aware of a proof utilizing some Z that is also alternating, but this breaks the condition that Z is strictly positive. I am unaware of an such sequence that has a limit of 0, all elements of the series are positive, yet is divergent.
This question is due within 10 hours. Please help!