Test the series for convergence or divergence

http://www.webassign.net/cgi-bin/symimag…

lim (2n-1)/(7n+1) = ____________
n-->infinity

Since lim (2n - 1)/(7n + 1) = 2/7 ≠ 0, the series diverges by the nth Term Test.

This limit is 2/7--which should be fairly obvious. The important thing is what this says about the associated series. Remember that a series Σ a_n can not be convergent if a_n doesn't go to zero as n goes to infinity. This is usually called the nth term test or the divergence test.

Since |a_n| -> 2/7 ≠ 0, the series diverges.