How do you determine if the series #ln(1/2) + ln(1/3) + ln(3/4) + ... +ln[k/(k + 1)] + ....# converges?
First of all I think there is a little mistake, the second term would be:
So it would be:
We can use an important logarithmic rule that says:
The first term is zero, all the other will cancel each other, but there is always another that survive. The bigger becomes