How do you determine the convergence or divergence of #sum_(n=1)^(oo) (-1)^(n+1)/n#?
1 Answer
The series is convergent and its sum is:
Explanation:
Leibniz's theorem states that a sufficient condition for the series with alternating signs:
to be convergent is that:
(i)
(ii)
Given:
We can actually calculate its sum starting from the MacLaurin development of the function
In fact:
and we can easily conclude that:
and for
so that the MacLaurin series is:
As