Make me an integral

Calculus Level 3

\[\lim_{n\to\infty}\left(\frac{1}{a+n}+\frac{1}{2a+n}+\frac{1}{3a+n}+\ldots+\frac{1}{na+n}\right)\]

Find the "closed form result" of the limit above.

Here, \(a\gt 0\) is an arbitrary constant such that the expression inside the limit is defined.

\[a\] \[e^a\] \[\dfrac{\ln(\sqrt{a}+1)}{a}\] \[\pi^a\] \[\dfrac{\ln(a+1)}{a}\] \[\pi^e\cdot \ln(a)\] \[\dfrac{\log_{10}(a+1)}{a}\] \[\dfrac{\ln(a+2)}{a}\]

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.