(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

So, I missed class the day Weierstrass M-test and cauchy criterion. I have a theorem for Weierstrass M-test, but the book gives no examples on how to use it. I figure cauchy criterion has to do with series, and states that a series is convergent if the partial sums is cauchy. If this one is wrong please let me know. I made it up, just now. We should be in the sequence and series of functions chapter, and there are is a lot of things that look cauchy (fn(x) - f(x)) < epsilon, but none called "cauchy criterion for series" like the email I get.

2. Relevant equations

Suppose {fn} is a sequence of functions defined on E, and {Mn} is a sequenc of nonnegative real numbers such that | fn(x) | <= Mn for all x in E, all positive integers n. If

the Sum Mn converges then the sum of fn converges uniformly.

3. The attempt at a solution

My guess is that how to use Weierstrass M test is sort of like a comparison test to derive uniform convergence. If you can get a series like 1/x^2 to converge and the sequence of functions is always less than 1/x^2, then the sequence of functions is uniformly convergent. Is this sounding right? There is no homework on this, so I don't have any examples to solve.

I'm really confused, they did a chapter in a day, which means I probably am not expected to get the entire depth down, but I get sad if I can't get it all the way.

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# Homework Help: Wierstrauss m test caucy criteria

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