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Math Help - calculus bc question

  1. #1
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    Question calculus bc question

    hi, i have a set of ap practice problems to do, and theres a topic on one of these questions that we havent covered in class. could anyone help me out please?

    which of the following series converge?
    I.) the summation from 1 to infinity of (k)/(n^2) where k is a constant
    II.) the summation from 1 to infinity of (-1)^n/(n^1/2)
    III.) the summation from 1 to infinity of (0.4)^(n-1)

    a.) I only
    b.) II only
    c.) III only
    d.) I and III
    e.) I, II, and III

    thanks so much
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  2. #2
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    Quote Originally Posted by holly123 View Post
    which of the following series converge?
    I.) the summation from 1 to infinity of (k)/(n^2) where k is a constant
    II.) the summation from 1 to infinity of (-1)^n/(n^1/2)
    III.) the summation from 1 to infinity of (0.4)^(n-1)

    a.) I only
    b.) II only
    c.) III only
    d.) I and III
    e.) I, II, and III
    all three series converge ...

    I. is a p-series, p > 1

    II. is an alternating series whose nth term approaches 0
    (conditionally converges ... has to be alternating in sign, otherwise it diverges)

    III. is a geometric series with |r| < 1

    you'll learn about all of these very soon.
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