How do you test the alternating series #Sigma (-1)^n/rootn n# from n is #[2,oo)# for convergence?
The alternating series:
is not convergent.
This is an alternating series so we can apply Leibniz's test stating that the series is convergent if given:
#lim_(n->oo) a_n = 0#
#a_(n+1)/a_n < 1#
Now consider the sequence:
The Leibniz's test is then not satisfied and the series is not convergent.