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**1. Homework Statement**

Convergent/Divergent?

Problem 1: infinite series, sigma(n=1) [1/((n^2)-n)

This one is clearly convergent, however it is undefined at n=1.

Is the whole problem undefined? Or is it convergent from (n=2)?

Problem 2: infinite series, sigma(n=1) [ln(n)/n]

This is divergent. It works with the Limit Comparison Test, but for some reason, I'm thinking I have to start by using sigma(n=2) [ln(n+1)/(n+1)] because, otherwise the first term would be zero. Can the test for a positive series include zero?

**2. Homework Equations**

Problem 1: Sn=(1/0)+(1/3)+(1/8)+...

Sn - undefined

Problem 2: Sn=(0/1)+(ln2/2)+(ln3/3)+...

(positive series?)

**3. The Attempt at a Solution**

Problem 1: Sn undefined => Series also undefined?

Problem 2: LCT, use b=(1/n), lim(n..inf) (a/b) = lim(n..inf) [(lnn/n)/(1/n)] = lim(n..inf) ln(n) = inf , limit > 0 , sigma (1/n) divergent, so sigma (lnn/n) divergent too.

Series divergent

**1. Homework Statement**

**2. Homework Equations**

**3. The Attempt at a Solution**