Anonymous asked in Science & MathematicsMathematics · 10 years ago

How do I solve: Determine whether the series ((1+(2^k))/ ((3^k)-1))?

Determine whether the series ((1+(2^k))/ ((3^k)-1)) CONVERGES OR DIVERGES


2 Answers

  • asimov
    Lv 6
    10 years ago
    Favorite Answer

    k=1 , 3/2

    k=2 , 5/8

    k=3 , 10/26

    the serie convergens to the asymptote 2^k/ 3^k = (2/3)^k

    and for k-->oo , (2/3)^k =0

    couse for every n , |n|<1 it will be convergens to 0

  • 10 years ago

    These terms converge to 0, because the terms are positive and dominated by (9/4)(2/3)^k, which go to 0.

    If you mean the sum of these terms, then the answer is still that it converges. This is because the sum with these dominating terms is a converging geometric series.

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