Math

how would I test this series for convergence of divergence?

the series from n=0 to infinity of

(n^2+1)/(n^3+1)

  1. 👍
  2. 👎
  3. 👁
  1. You can do the Integral test. You see that the Series diverges logarithmically.

    Exercise: Try to compute the large N asymptotics of

    n=0 to N of

    (n^2+1)/(n^3+1)

    For large N the summation will be:

    1/3 Log(N) + a + b/N + c/N^2 + ...

    Try to find out what a, b, c etc. are.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Which of the following series could be tested for convergence/divergence with the integral test? the summation from n=1 to infinity of 1/n! the summation from n=1 to infinity of 1/n the summation from n=2 to infinity of ln(n)/n^2

  2. calculus 2

    Test the series for convergence/divergence. The Summation from n=1 to infinity of: 1*3*5...(2n-1)/(2*5*8...(3n-1) I'm not sure what to do with the extra terms on the left.

  3. calc

    use the root test to to determine the convergence or divergence of the series 100n/e^n

  4. Calculus - Alternating Series Test

    Determine whether the infinite series, sigma(((-1)^(n+1))/n)^2 converges or diverges. My professor gave these in a problem set after he taught the alternating series test. Simplying the series we get, sigma(((-1)^(n+1))/n)^2

  1. Integral Calculus

    For what values of p is this series convergent? (summation from n = 1 to infinity) of ((-1)^(n-1))/(n^(p + 2)) A. p >= -2 B. p =/= -2 C. p > -2 D. for all p E. p > 0 You have to use the Alternating Series Test. I've already tried

  2. calculus

    determine if the series is absolutely convergent and convergent the sum from n=1 to infinity of sin(n^2)/n^2 what series test should I use and how? the ratio test?

  3. Calculus

    Use the Integral test to determine whether the series is convergent or divergent. infinity "series symbol" n=1 (ne^(n"pi")) Note: I don't know how to solve or work out so show all your work. And give the answer in EXACT FORM

  4. calculus II

    (a) Use differentiation to find a power series representation for f(x) = 1/(5 + x)^2 What is the radius of convergence, R? (b) Use part (a) to find a power series for f(x) = 1/(5 + x)^3 What is the radius of convergence, R? (c)

  1. calculus

    test the series for convergence or divergence using the alternating series test the sum from n=1 to infinity of (-1)^n/(3n+1) I said it converges, is this true?

  2. calculus

    test the series for convergence or divergence the series from n=0 to infinity of (x^2+1)/(x^3+1) I said that due to the limit comparison test this converges at 1

  3. calculus

    test the series for convergence or divergence the series from n=1 to infinity of 1/(arctan(2n)) I again didn't know what test to use

  4. calculus

    test the series for convergence or divergence. the sum from n=1 to infinity of ((-1)^n*e^n)/(n^3) I said it converges because the derivative of (1/n^3) is decreasing

You can view more similar questions or ask a new question.