How to evaluate infinite series 1/n

This series diverges.



Notice that this series essentially gives the left-endpoint Riemann sum approximation to the integral



Because is strictly decreasing for , it follows that this approximation is greater than or equal to the value of the integral:



So if the integral diverges, then so must the finite series. You have




and thus the series must also diverge.

12x+8-x=12x-x+8=11x+8=11