How do you use the Nth term test on the infinite series #sum_(n=1)^ooln((2n+1)/(n+1))# ?
By the nth term test (Divergence Test), we can conclude that the posted series diverges.
Recall: Divergence Test
Let us evaluate the limit.
by squeezing the limit inside the log,
by dividing the numerator and the denominator by
By Divergence Test, we may conclude that
Caution: This test does not detect all divergent series; for example, the harmonic series