Consider the infinite geometric series below. a. Write the first 4 terms of the series b. Does the series diverge or converge? c. If the ser

Question

Consider the infinite geometric series below. a. Write the first 4 terms of the series b. Does the series diverge or converge? c. If the series has a sum, find the sum. ∑ [infinity] n=2 (− 2) n−1

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Emery 3 weeks 2021-09-07T01:30:44+00:00 1 Answer 0

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    2021-09-07T01:32:37+00:00

    Answer:

    Step-by-step explanation:

    Given the geometrical series

    ∑ [infinity] n=2 (− 2) n−1

    I think the correct series should be the sum from n = 2 to ∞ of (-2)^n-1

    So,

    ∑(-2)^(n-1)…… From n = 2 to ∞

    A. The first four terms

    When n = 2

    (-2)^(2-1) = (-2)^1 = -2

    When n = 3

    (-2)^(3-1) = (-2)^2 = 4

    When n = 4

    (-2)^(4-1) = (-2)^3 = -8

    When n = 5

    (-2)^(5-1) = (-2)^4 = 16

    B. The series will diverge since the common ratio is not between 0 and 1

    So, let use limit test

    Lim as n →∞ (-2)^(n-1) = (-2)^∞ = ±∞

    Since the limit is infinite, then the series diverges

    C. Since her series diverges we can find the sum, the sum is infinite, so it will sum up to ±∞

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