Calculus  Series
posted by Shaniquaa on .
Why is the limit of the sum n=1 to infinity of ln(2(n+1))â€“ln(2n) divergent? I thought it would be ln2 because all the other terms cancel out cancel out.

L'Hopitals rule:
(1/2n+2)(2n/1)
2n/(2n+2)
second application of the rule:
2/2=1
so at infinity, you are adding 1 + 1+ ...
which means it is divergent.