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Ankit Jaiswal
:
please guys help me out What is the sum of infinite terms of a series whose nth term is n/(n^2+4)
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August 30, 2016 at 6:20am
Little Sky
:
[link]http://ecademy.agnesscott.edu/~lriddle/apcalculus/approxSeries.pdf[/link] Pay attention to example 2. You will need integration.
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August 30, 2016 at 11:29am
Shu Yun
:
it's a convergent series as it's limit is to zero. for an easy way out, use integration formula: [ieqn]\int\frac{x}{x^{2}+a^{2}} dx= \frac{1}{2}\ln\left| x^{2}+a^{2} \right| [/ieqn] where x is n, a is 2
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August 30, 2016 at 2:34pm
Little Sky
:
The series actually converges. However, its sum diverges. Once you integrate it and you have natural long something, as n tends to infinity, so does natural log n^2, not to mention natural log (n^2 + 4). [link]https://www.math.hmc.edu/calculus/tutorials/convergence/[/link]
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August 31, 2016 at 1:19am
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