(-1)*+1 1 = 4 ) 2n – 1 n=1 = 4 -+- + - 8.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. The series
Σ
(-1)*+1
= 4 – +- + - ..
= 4
2n – 1
n=1
was discovered by Gregory and Leibniz in the late 1600s. This
result follows from the Maclaurin series for f(x)= tan-1 x. We will
discuss this series in the next chapter.
a. Prove that this series converges.
b. Evaluate the partial sums S„for n=10. 20. 50. 100.
C. Use the iemainder estimate for alternating series to get a bound
on the error R,.
d. What is the smallest value of N that guarantees |RN| <0.01?
Evaluate Sy.
Transcribed Image Text:1. The series Σ (-1)*+1 = 4 – +- + - .. = 4 2n – 1 n=1 was discovered by Gregory and Leibniz in the late 1600s. This result follows from the Maclaurin series for f(x)= tan-1 x. We will discuss this series in the next chapter. a. Prove that this series converges. b. Evaluate the partial sums S„for n=10. 20. 50. 100. C. Use the iemainder estimate for alternating series to get a bound on the error R,. d. What is the smallest value of N that guarantees |RN| <0.01? Evaluate Sy.
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