Find the Following Sum!
Calculus
Level
3
Evaluate
\[ \lim_{N\to\infty} \left(\frac{1}{2N}+\frac{1}{2N+1}+\frac{1}{2N+2}+\frac{1}{2N+3}+\dots+\frac{1}{3N}\right).\]
The answer is of the form \(\ln \frac{a}{b},\) where \(a\) and \(b\) are coprime positive integers.
Find \(a+b\).
by
Nick Turtle