I was wondering if we would use the Ratio Test on this series? If not any ideas?
Sigma: 2.4.6.....(2n) divided by 3.5.7.....(2n+1)
Use the inequality
then do direct comparison with the harmonic series.
Edit: you can prove the inequality by induction on n.
proves it true for n=1.
Now assume it is true for .
and the induction is complete.