Series Rearrangement

Question

I have two proofs for a real analysis class that I'm struggling with.

The first says,

Prove: $\frac{1}{3n-2}+\frac{1}{3n-1}-\frac{1}{3n}>\frac{1}{3n}$ for $n= 1, 2, ...$ and deduce that $1+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...$ is divergent.

Neurax

Answer 1

Hint: The first two terms have smaller denominators than $\frac 1{3n}$ Smaller denominator makes a bigger number.