How do you use the Nth term test on the infinite series #sum_(n=2)^oon/ln(n)# ?
The Nth Term Test is a basic test that can help us figure out if an infinite series is divergent. It states that if the
Using this test with our series, we have:
If we replace
#oo/ln(oo) = oo/oo#
Since we have an Indeterminate Form of
#lim_(n->oo) 1/(1/n) = lim_(n->oo) n = oo#
Because we end up with a non-zero answer, we know that the series diverges.