calculus - ratio test

Posted by COFFEE on Sunday, July 29, 2007 at 6:32pm.

infinity of the summation n=1: (e^n)/(n!) [using the ratio test]

my work so far:

= lim (n->infinity) | [(e^n+1)/((n+1)!)] / [(e^n)/(n!)] |

= lim (n->infinity) | [(e^n+1)/((n+1)!)] * [(n!)/(e^n)] |

= lim (n->infinity) | ((e^n)(e^1)(n!)) / ((n+1)(n!)(e^n)) |
..the e^n & n! cancels out

= lim (n->infinity) | (e^1) / (n+1) |

im stuck here.. how do i finish this?
and also to find out if it's Divergent (L>1), convergent (L<1), or fails (L=1)?

For Further Reading

* Calculus - ratio test - Count Iblis, Sunday, July 29, 2007 at 7:01pm

The limit is zero. So, L = 0 therefore the series is convergent.

The value of the summation is e^e - 1

-------------------

thank you for your response, but..

how did you get the summation of e^(e-1)
...from this?
= lim (n->infinity) | (e^1) / (n+1) |

  1. 👍 0
  2. 👎 0
  3. 👁 213
asked by COFFEE

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus - ratio test

    infinity of the summation n=1: (e^n)/(n!) [using the ratio test] my work so far: = lim (n->infinity) | [(e^n+1)/((n+1)!)] / [(e^n)/(n!)] | = lim (n->infinity) | [(e^n+1)/((n+1)!)] * [(n!)/(e^n)] | = lim (n->infinity) |

    asked by COFFEE on July 30, 2007
  2. 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

    asked by Alice on May 13, 2019
  3. English

    1. What day is July 22? - It is Sunday. 2. What day is on July 22? - It is Sunday. ============== Which one is right? 3. On July 22, Sunday, what did they do? 4. On Sunday, July 22, what did they do? 5. On July 22, on Sunday, what

    asked by rfvv on December 1, 2015
  4. CALC 2

    In the following series x is a real number. In each case, use the ratio test to determine the radius of convergence of the series. Analyze the behavior at the endpoints in order to determine the interval of convergence. a.

    asked by Bae on April 13, 2014
  5. CALC 2 pls help!!

    In the following series x is a real number. In each case, use the ratio test to determine the radius of convergence of the series. Analyze the behavior at the endpoints in order to determine the interval of convergence. a.

    asked by BAE on April 14, 2014
  6. Calculus 2

    In the following series x is a real number. In each case, use the ratio test to determine the radius of convergence of the series. Analyze the behavior at the endpoints in order to determine the interval of convergence. a.

    asked by BAE on April 14, 2014
  7. Calculus - ratio test

    infinity of the summation n=1: (e^n)/(n!) [using the ratio test] my work so far: = lim (n->infinity) | [(e^n+1)/((n+1)!)] / [(e^n)/(n!)] | = lim (n->infinity) | [(e^n+1)/((n+1)!)] * [(n!)/(e^n)] | = lim (n->infinity) |

    asked by COFFEE on July 29, 2007
  8. Calculus - Second Order Differential Equations

    Posted by COFFEE on Monday, July 9, 2007 at 9:10pm. download mp3 free instrumental remix Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8))

    asked by COFFEE on July 10, 2007
  9. PHYSICS, still cant get it

    A man (weighing 915 N) stands on a long railroad flatcar (weighing 2805 N) as it rolls at 18.0 m/s in the positive direction of an x axis, with negligible friction. Then the man runs along the flatcar in the negative x direction

    asked by COFFEE on February 27, 2007
  10. Intermediate Accounting

    The 10% bonds payable of Klein Company had a net carrying amount of $570,000 on December 31, 2006. The bonds, which had a face value of $600,000, were issued at a discount to yield 12%. The amortization of the bond discount was

    asked by Jeniffer on February 11, 2010

More Similar Questions