# How do you show that the series #ln1+ln2+ln3+...+lnn+...# diverges?

##### 2 Answers

May 30, 2018

We can immediately rewrite as

#S = ln(1 * 2 * 3 * 4 * 5* 6 * 7 * ...)#

#S = ln(n!)#

If we take the limit of the sum as

Hopefully this helps!

May 30, 2018

By the (nth-term) divergence test:

So the series diverges