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

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.

    posted by rich

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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?
  2. 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
  3. 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?
  4. 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?
  5. 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?
  6. 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
  7. Calculus

    For what values of p>0 does the series Riemann Sum [n=1 to infinity] 1/ [n(ln n) (ln(ln n))^p] converge and for what values does it diverge? You need to let the summation start at n = 3 to avoid the singularity at n = 1
  8. 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)
  9. calculus

    A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)sqrt(x+1)(<or=)10? B) So once that is found, then how can you prove that if 0(<or=)u(<or=)v(<or=)10, then
  10. 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

More Similar Questions