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Math Help - Series convergence test

  1. #1
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    Series convergence test

    The problem is asking to prove that the series either converges or diverges. I think I know how to prove divergence but I need someone to confirm. The series is the sum from 1 to infinity of:

    (2^(n-1)+1)/2^n

    Given that the sum does diverge (right?), you can simplify and say that the original problem, for all values of N > 1, is greater than (2^(n-1))/2^n. Since that equation always yields a value a 1/2, the sum diverges, and since the original sum is greater than that, it must diverge too. Is everything correct?
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Tbone456 View Post
    The problem is asking to prove that the series either converges or diverges. I think I know how to prove divergence but I need someone to confirm. The series is the sum from 1 to infinity of:

    (2^(n-1)+1)/2^n

    Given that the sum does diverge (right?), you can simplify and say that the original problem, for all values of N > 1, is greater than (2^(n-1))/2^n. Since that equation always yields a value a 1/2, the sum diverges, and since the original sum is greater than that, it must diverge too. Is everything correct?
    Yes
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