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

Показать описание

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.

Zak's Lab

Рекомендации по теме

Комментарии

Thank you so much. My calculus professor is incapable of explaining things clearly. This finally made the b_n selection process click!

raiguard

Doesn’t this technic tells us that if 0<c<infinity then both series converge or both diverge? In this case c=0 so wouldn’t it diverge?

samgag

so what you're saying is that we essentially... go for two options that give two diff results and aim for something in between?

curtistrinh

I wonder why we have to convert to f(x) before using l'hopitals

curtistrinh

One can also use integral test to show that it is convergent.

josephdewuhan

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

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

Sum (ln(n)/n^2) weird limit comparison to 1/n^(3/2) motivation. L'Hopital's rule limit co...

10.6j Limit Comparison Test, Infinite Series, ln(n)/n^(7/2), Example - AP Calculus BC

Limit Comparison with SUM ln(n)/n^3 (Convergent or Divergent Series 23)

Determine whether series converges or diverges (ln n)/n. Use appropriate test

3 Decreasing Series ln n over n

Integral Test vs. Comparison Test: ln(n)/n^2 vs ln(n)/n^4

Alternating Infinite Sum of ln(n)/n^2

Calculus 2: Solving Exam 3 -All things SEQUENCES & SERIES! -Fall 2019 Part 1| Math with Profess...

Comparison Test | Series Converges or Diverges | Sum 1/ln(n) , n= 2 to infinity

Infinite Series Sum (ln(n/2))

Infinite Series SUM( ln(n/(2n + 5) ) || Does it Converge or Diverge?

Direct comparison test 1/(ln(n)), including derivative proof that ln(n) is less than n. Sum 1/ln(n).

Series ln n /e^n as n approaches to infinity Converges or Diverges Math Proof |Mad Teacher

Sum from n=2 to infinity of 1/(ln n)^(ln n)

Determine if sequence converges or diverges, if converges find limit {(ln n)^2/n}

Determine if series is absolutely, conditionally convergent or divergent { (-2)^n/(n ln n) }

Does the Series SUM(ln(n/(2n + 5)) Converge or Diverge?

100 series convergence tests (no food, no water, no stop)

Series Convergence Integral Test lnn / n

Calculus- Series (-1)^n/(n ln^2(n)) (integral test)

Determine the convergence or divergence of the series (n ln n)/ (2^n). Ratio Test. L’Hopital’s Rule...

Sum from n=1 to infinity of ln(n)/n!

Calculus Help: Divergent and Convergent- Summation 2(ln n)^3 / n - (Part 2) - Integral Test