Actually what you want using the ratio test is
which gives or . Then check your endpoints giving the two series
and
Then determine the convergence of each one to determine whether these endpoints should be included in your interval.
Hi,
I have the following question:
Part d
Using appropriate series convergence tests, prove that the series
converges if and only if the real number satisfies
So my current working is this:
Let , then
Now as tends to infinity, will tend to .
Therefore, by the ratio test:
If , the series converges
If , the series diverges
If ,
In part b of this same question, we had to prove that diverges, which I did successfully.
According to my working then, the series converges if , which only partly satisfies the requirement:
Can someone spot what I've done wrong here?
Thanks
Note: In part c of the same question, we had to state and prove the Alternating Series Test, which I did successfully, so I'm thinking that we're meant to apply it here somehow, but I'm not sure how.
Actually what you want using the ratio test is
which gives or . Then check your endpoints giving the two series
and
Then determine the convergence of each one to determine whether these endpoints should be included in your interval.
Thanks.
According to Alternating series test - Wikipedia, the free encyclopedia, the Alternating Series Test is from , not . Does this make a difference?
I previously knew the Alternating Series Test as
Is this the same as what Wikipedia says?
Thanks again