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? asked in Science & MathematicsMathematics · 7 years ago

How do I determine (1/2) + (1*3/2*5) + (1*3*5/2*5*8) ... is converge or diverge?

Use ratio test to determine whether the following series converge or diverge

(1/2) + (1*3/2*5) + (1*3*5/2*5*8) + (1*3*5*7/2*5*8*11) ...

2 Answers

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  • Brian
    Lv 7
    7 years ago
    Favorite Answer

    The nth term of the series has the form

    a(n) = [1*3*.....*(2n - 1)] / [2*5*....*(3n - 1)].

    Thus a(n+1) / a(n) = (2*(n+1) - 1) / (3*(n+1) - 1) =

    (2n + 1) / (3n + 2), and so

    lim(n->infinity) la(n+1) / a(n)l = 2/3 < 1,

    thus by the ratio test the series converges.

  • ?
    Lv 7
    7 years ago

    ratio is 3/5 then 5/8 approaches 2/3 so it converges.

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