How do you determine the convergence or divergence of #Sigma ((-1)^(n+1)n)/(2n-1)# from #[1,oo)#?
1 Answer
Dec 23, 2016
The series:
is divergent.
Explanation:
You can determine whether an alternating series converges using Leibniz' criteria, which states that:
converges if:
(i)
#a_n>a_(n+1)#
(ii)#lim_n a_n = 0#
As the general term of the series above can be expressed as:
We can quickly see that:
so that condition (ii) is not met and the series is divergent.