Let 2 (-1)** 'ak be a convergent alternating series with terms that are nonincreasing in magnitude. Let R, = S-S, be the remainder in approximating the value of that series by the sum of k=1 its first n terms. Then R,san+1. In other words, the magnitude of the remainder is less than or equal to the magnitude of the first neglected term. For the convergent alternating series (-1)% -, evaluate the nth partial sum for n=2. Then find an upper bound for the error s-S, in using the nth partial sum S, to estimate the value of the series S. 00 k=0 (6k + 1)*

Let 2 (-1)** 'ak be a convergent alternating series with terms that are nonincreasing in magnitude. Let R, = S-S, be the remainder in approximating the value of that series by the sum of k=1 its first n terms. Then R,san+1. In other words, the magnitude of the remainder is less than or equal to the magnitude of the first neglected term. For the convergent alternating series (-1)% -, evaluate the nth partial sum for n=2. Then find an upper bound for the error s-S, in using the nth partial sum S, to estimate the value of the series S. 00 k=0 (6k + 1)*

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.4: Series And Their Notations

Problem 55SE: The sum of an infinite geometric series is five times the value of the first term. What is the...

See similar textbooks