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(2) A series is said to be "alternating" if the signs of subsequent terms switch between positive and negative. Typically, alternating series have a factor of (-1)" to make the signs switch between terms. (a) To further explore this idea, write out the first six terms of the following series: (-1)" n! n=0

(2) A series is said to be "alternating" if the signs of subsequent terms switch between positive and negative. Typically, alternating series have a factor of (-1)" to make the signs switch between terms. (a) To further explore this idea, write out the first six terms of the following series: (-1)" n! n=0

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 23RE: Use the formula for the sum of the first ii terms of an arithmetic series to find the sum of the...
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(2) A series is said to be "alternating" if the signs of subsequent terms switch between positive and negative. Typically, alternating series have a factor of (-1)" to make the signs switch between terms. (a) To further explore this idea, write out the first six terms of the following series: (-1)" n! n=0 (b) Now, use the ratio test to determine if this series converges: (c) For this question, navigate to the Wolfram Alpha website (wolframalpha.com) and type the series from part (a) into the search bar. You should be able to use written words like, "The sum from n=0 to infinity of..." (this is the method I typically use), or you can type some math text such as sum_ (n=0)^infinity to refer to the sum. What do you notice about the results you get?
Transcribed Image Text:(2) A series is said to be "alternating" if the signs of subsequent terms switch between positive and negative. Typically, alternating series have a factor of (-1)" to make the signs switch between terms. (a) To further explore this idea, write out the first six terms of the following series: (-1)" n! n=0 (b) Now, use the ratio test to determine if this series converges: (c) For this question, navigate to the Wolfram Alpha website (wolframalpha.com) and type the series from part (a) into the search bar. You should be able to use written words like, "The sum from n=0 to infinity of..." (this is the method I typically use), or you can type some math text such as sum_ (n=0)^infinity to refer to the sum. What do you notice about the results you get?
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