In one or two sentences

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

In one or two sentences, explain why knowing an upper bound

M

for

|f^{(n+1)}(z)|

on the interval between

a

and

x

guarantees that the magnitude of the remainder

|R_n(x)|

does not exceed a computable constant.