Given the following sequence of partial sums:
My attempt:
If I can find the series for this sequence of partial sums, then I can test the series to see if it's convergent or divergent.
Thus:
Since :
But this is as far as I got.
I would like to express this with a factor so that I can use the alternating series test, but I'm not sure how exactly.
Would this be correct?
This is the question in its entirety:
For a series the sequence of partial sums is . Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
Hint: Find the series n'th term and express it as an alternating series.
(It's supposed to be an infinity sign above the sum, but for some reason LATEX doesn't want to display it)
Great! Now I get it
So by using the alternating series test, it can be shown that the series is convergent.
And to test for absolute convergence, using the comparison test:
Since is divergent, then the absolute of is divergent too, thus it is not absolutely convergent.
So conclusion would be that it's conditionally convergent?
Would the absolute value of the fraction be or ? I wasn't quite sure about that.