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October 30th, 2016, 08:09 AM   #1
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Question Series Convergence

If you are using the integral test to find if a series is convergent or divergent, and find the integral converges to a negative number, does that mean the series still converges.
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October 30th, 2016, 08:24 AM   #2
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The integral test operates on positive, monotonic functions only (from memory). You should investigate the integral of $|f(x)|$ to see if the series is absolutely convergent.

Last edited by v8archie; October 30th, 2016 at 08:30 AM.
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October 31st, 2016, 08:21 AM   #3
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Integral Test

Let f(x) be positive, continuous , and non-increasing for x$\displaystyle \geq$ N and a$\displaystyle _{n}$ =f(n) for n$\displaystyle \geq$N.
Then a$\displaystyle _{n}$ converges or diverges according as $\displaystyle \int_{N}^{\infty}$f(x)dx converges or diverges.
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