Hi, I've been thinking about the comparison test for integrals. Usually when I have an integrand where the denominator is f(x) + something positive I can usually find a suitable bound without much trouble. However when the denomoninator of the integrand is f(x) - something positive finding a bound is generally more difficult. This is because I would generally have no idea as to whether the integral converges or not.(adsbygoogle = window.adsbygoogle || []).push({});

So one day I was thinking about the limit comparison test which comes in handy when I have series' where the denominator is something like 2^n - 1. Long story short I used the limit comparison test with integrals by considering the integral as a series(in the mathematically incorrect way) and for a few examples it seemed to work. For example if I have a integral where the integrand is of the form 1/(f(x) - c), c > 0 I just wrote the series(I've omitted the sigma etc) 1/(f(n) - c) and used the limit comparison test for series to determine whether or not the series 1/(f(n)-1) converges. In the few examples I tried, if the corresponding series converges I've also found that the integral converges.

Can the limit comparison test for series be used as a test for integrals in this way? I know that there is an integral test for series but I'm not sure if there is anything the other way around.

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# Homework Help: Integral convergence and limit comparison test

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