Question

evaluate\[\sum_{n=1}^{\infty}{\ln(\frac{n}{n+1})}\]

Answer 1

integral test says that this series does not converge.

Answer 2

i was checking it .. are you sure about it ?

Answer 3

ln(n/(n+1)) = -ln(1 + 1/n) = -( 1/n - 1/2n^2 + .... ), which is approx = -1/n and
the sum of that series diverges, so it makes sense this one does as well.