Let be a convergent series of positive terms. What can be said about the convergence of ? My Attempt: Therefore, is a divergent harmonic series?
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Hi, Originally Posted by RedBarchetta You can't do this, depends on ! Hint : for all , because for all .
Originally Posted by RedBarchetta Let be a convergent series of positive terms. What can be said about the convergence of ? My Attempt: Therefore, is a divergent harmonic series? What about this
Originally Posted by Mathstud28 What do you mean by ?
Last edited by flyingsquirrel; Nov 15th 2008 at 02:32 PM. Reason: ...
Originally Posted by flyingsquirrel What do you mean by ? Sorry, I misread the problem. But here is how I would present the solution Since this is a decreasing sequence of positive numbers let us apply Cauchy 'sCondensation test. converges iff converges. From there it should be pretty obvious what the answer is.
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