Colin O'Haire, Math Teacher at Rocklin high school, Numerade Educator

01:22

Thomas Calculus

Recall that the Maclaurin series is just another name for the Taylor series at $x=0 .$ Each of the series in Exercises $31-34$ is the value of the Maclaurin series of a function $f(x)$ at some point. What function and what point? What is the sum of the series?
$$
1-\frac{\pi^{2}}{4^{2} \cdot 2 !}+\frac{\pi^{4}}{4^{4} \cdot 4 !}-\cdots+\frac{(-1)^{k}(\pi)^{2 k}}{4^{2 k} \cdot(2 k !)}+\cdots
$$

Chapter 11: Infinite Sequences And Series

Section 9: Convergence of Taylor Series; Error Estimates