Calculus

posted by .

Show that the following series is absolutely convergent:

Summation from 1 to infinity:

[(-1)^n * (n+1) * 3^n]/ [2^(2n+1)]

I've done the ratio test and replaced n in this series with n+1. I get 3/4 in the end, which is less than 1, which confirms that the series is abs. convergent, but when I put it in the calculator the answer is 0. Can someone do this problem and show me where I might have made a mistake?

Thank you

  • Calculus -

    ratio test:
    k(n)/k(n+1)

    Redo your ratio test.

Respond to this Question

First Name
School Subject
Your Answer

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) | ((e^n)(e^1)(n!)) …
  2. 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)!)] …
  3. 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) | ((e^n)(e^1)(n!)) …
  4. calculus

    determine if the series is absolutely convergent and convergent. the sum from n=0 to infinity of ((-1)^n*e^n)/(n!) I used the ratio test and said that it was absolutely convergent and convergent. is this true?
  5. calculus

    determine if the series is absolutely convergent and convergent. the sum from n=0 to infinity of ((-1)^n*e^n)/(n!) I used the ratio test and said that it was absolutely convergent and convergent. is this true?
  6. 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?
  7. calculus

    for each series determine if the series is absolutely convergent and convergent the sum from 0 to infinity of (-1)^n/(the square root of (n+1)) I did the ratio test and got -1, which is less than 0 making it absolutely convergent, …
  8. calculus

    for the series is absolutely convergent and convergent the series from 1 to infinity of (x^3)/(5^x) i did the ration test and get absolutely convergent and convergent is this correct?
  9. calculus

    does this series converge, and if so is it absolutely convergent?
  10. calculus

    does this series converge, and if so is it absolutely convergent?

More Similar Questions