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

  1. 👍 0
  2. 👎 0
  3. 👁 58
asked by laura
  1. Hi:

    The series is alternating of the form(a_n)*(-1)^n, where a_n = e^n/n^3. Because limit (n->inf)[a_n] not= 0 (a_n->inf as n->inf}, the series diverges.

    Regards,

    Rich B.

    1. 👍 0
    2. 👎 0
    posted by rich

Respond to this Question

First Name

Your Response

Similar Questions

  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?

    asked by laura on February 29, 2008
  2. 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?

    asked by sarah on February 27, 2008
  3. math

    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?

    asked by sarah on February 28, 2008
  4. Calculus

    Determine convergence or divergence for the following series. State the tests used and justify your answers. Sum (infinity, n=1) 1/(1+e^-n) Sum (infinity, n=1) (2*4*6...2n)/n! Sum (infinity, n=0) (n-6)/n Sum (infinity, n=0)

    asked by Jade on March 4, 2013
  5. math

    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

    asked by sarah on February 28, 2008
  6. 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 is this true?

    asked by sarah on February 27, 2008
  7. CALC 2

    a. Consider the following limit as a fact: lim n-> infinity ((n!)^1/n)/n = 1/e Use this limit to study the convergence of this series using the root test. Sum of infinity and n=1 of ((3^n)n!)/n^n b. Use the ratio or the root test

    asked by Bae on April 7, 2014
  8. 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

    asked by lila on March 16, 2008
  9. Math

    How would I test this series for convergence of divergence? the series from n=0 to infinity of sin(2^(-n))

    asked by Anna on March 6, 2008
  10. Math

    one last one, so sorry! thanks so much! how would I test the series for convergence or divergence? the series from n=1 to infinity of 1/(arctan(2n))

    asked by Anna on March 6, 2008

More Similar Questions