Weierstrass M-test of Uniform convergence

Weierstrass M-test 

Uniform convergence of Sequences and Series of Functions 

It should be noted carefully that uniform convergence of a function sequence {fn(x)}is a property associated with a domain of x comprising more than one point whereas simple convergence is meaningful at each point of that domain in the sense that it reduces to a convergence of sequence of constants.

Weierstrass M-test