# 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
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

## 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)

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