Limit comparison test (ln(n)/n)^2. Weird comparison 1/n^(3/2) explained by looking at 1/n and 1/n^2. скачать в хорошем качестве

Limit comparison test (ln(n)/n)^2. Weird comparison 1/n^(3/2) explained by looking at 1/n and 1/n^2.

New videos every week! Subscribe to Zak's Lab    / @zakslab   Questions or requests? Post your comments below, and I will respond within 24 hours. We test the convergence of (ln(n)/n)^2 with a weird limit comparison test with L'Hopital's rule, including the motivation for limit comparison to 1/n^(3/2). This limit comparison seems weird, but we motivate the successful comparison by looking at two inconclusive comparisons: one limit comparison to the harmonic series and one limit comparison to 1/n^2. Both of these are inconclusive for opposite reasons -- our terms are smaller than the divergent series, but larger than the convergent series. Finally, we try a comparison in between: the weird comparison 1/n^3/2 and we successfully show that the series converges by the limit comparison test.