How do you determine the convergence or divergence of #Sigma ((-1)^(n))/(ln(n+1))# from #[1,oo)#?
1 Answer
Feb 2, 2017
The series:
is convergent.
Explanation:
The series:
is an alternating series, so we can test its convergence using Leibniz's theorem, which states that an alternating series
is convergent if:
(i)
#lim_(n->oo) a_n = 0# (ii)
#a_(n+1) <= a_n#
in our case:
and since
also the second condition is satisfied.