Question

Can somebody explain to me the difference between the Weirstrass M-test and the Direct Comparison Test? They seem like the exact same thing to me practically.

Answer 1

To me, Weirstrass M-test indicates to uniform convergent while Comparison test is just for convergent only.
Uniform convergent series, \(lim_{x--> x_0} f(x) =f(x_0)\) that is when \(|x-x_0|<\delta_0\) \(|f(x) - f(x_0)|<\varepsilon\) and \(\delta_0\) depends on \(x_0\)
while in Comparison test \(\delta\) depends on \(\varepsilon\)

Answer 2

Thank you!