Calculus

If you have a geometric alternating series, and you prove that the series is converging by doing geometric series test, and NOT alternating series test, then does that allow you to say that the series converges ABSOLUTELY?
Or should you do alternate series test also to say that it converges absolutely? I was confused because I know that ratio test and root test allows you to say that it converges absolutely without doing the alternate integral test.
What about the other tests like comparison tests and integral test?

Thanks!

If it is a geo alternating, then proof of the geometric convergence test is sufficent for absolute convergence.

Any test, and there are several, that says the series converges absolutely is sufficent: others are not required.

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Which of the following statements is true for the series the summation from n=0 to infinity of (-1)^n and 5/4^n? a) The series diverges because it is geometric with r = 5/4 and a = –1. b) The series converges to 4 because it is

  2. Calculus

    Which one of the following statements is true about the series the series from n equals 1 to infinity of the quotient of negative 1 raised to the nth power and n ? (4 points) Is this A or B? I am a little confused. A) It is

  3. Algebra 2

    Describe an infinite geometric series with a beginning value of 2 that converges to 10. What are the first four terms of the sequence? a{1} = first term of series ∞ Infinite Sum = ∑ a{1} • r^(n – 1) = a{1} ⁄ (1 – r)

  4. math B30

    If the seventh term of a geometric series is 192, and the first term is 3, find the sum of the first 8 terms of the series

  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?

  2. Calculus

    Consider the series 1/4+1/6+1/9+2/27+4/81+.... Does the series converge or diverge? Is the series arithmetic, geometric, neither, or geometric with an absolute value of the common ration being greater/ less than 1?

  3. Algebra

    Is the series 72, 48, 32,... an arithmetic or geometric series. WHat is common difference or ratio

  4. algebra

    consider the infinite geometric series n=1 -4(1/3)^n-1 . i need help with writing the first four terms of the series and finding the sum if it has a sum.

  1. Math

    The first two terms in a geometric series is 12. The sum of the first three terms of the same series is 62. Determine the first four terms of the series.

  2. math

    in a geometric series t1=23,t3=92 and the sum of all of the terms of the series is 62 813. how many terms are in the series?

  3. Math calculas 2

    Trying to review for the exam. Can someone please help me with this series questions. Thank you Use geometric series test to determine whether converges or diverges if it converges find the sum ∞ ∑. (π/2)^n n=1 ∞ ∑.

  4. Chemistry

    Hydrogen exhibits several series of line spectra in different spectral regions. For example the Lyman series (nf = 1 in Balmer-Rydberg equation) occurs in the ultraviolet region while the Balmer (nf = 2) series occurs in the

You can view more similar questions or ask a new question.