Proof
Let be the limit of the sum . Since the sum is absolutely convergent, call its limit .
By convergence of the sum, for there exists an integer such that . We will show that converges uniformly by showing that . The crucial point here is that does not depend on .
Read more about this topic: Weierstrass M-test
Famous quotes containing the word proof:
“Talk shows are proof that conversation is dead.”
—Mason Cooley (b. 1927)
“War is a beastly business, it is true, but one proof we are human is our ability to learn, even from it, how better to exist.”
—M.F.K. Fisher (1908–1992)
“The thing with Catholicism, the same as all religions, is that it teaches what should be, which seems rather incorrect. This is “what should be.” Now, if you’re taught to live up to a “what should be” that never existed—only an occult superstition, no proof of this “should be”Mthen you can sit on a jury and indict easily, you can cast the first stone, you can burn Adolf Eichmann, like that!”
—Lenny Bruce (1925–1966)