Question

How to prove the pointwise convergence of the sequence with sup norm?

Answer 1

Answer:

Theorem: If is a convergent sequence, that is $\lim_{n \to \infty} a_n = L$ for some , then is also bounded, that is for some , $\mid a_n \mid ≤ M$. So if , then $\mid a_n \mid < 1 + \mid L \mid$.