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Given the power series expression E n A xln + 2) n = 1 + 2 3 A x" n = 1 1. Force the first power series to have a simple exponent. 2. Make sure that the power series start at the same value for n. 3. Combine the two power series together into a single power series. 00 (A R = 1 00 ® 2 [3 (R - 2) A, ] * B R = 1 © 34, x' + 6A,x2 + E [3RA * Σ R = 3 00 E (R - 2) A (a - 2) + 34,]* ЗА R = 1 00 ® 34, x! + 3A, x² + 2 [[R - 2) A (r - 2) + 3 A (R- 2) R = 3 00 © -34, + E [3(r - 2) A ] =* E [3 (R – 2) A,] × (F R = 3

Given the power series expression E n A xln + 2) n = 1 + 2 3 A x" n = 1 1. Force the first power series to have a simple exponent. 2. Make sure that the power series start at the same value for n. 3. Combine the two power series together into a single power series. 00 (A R = 1 00 ® 2 [3 (R - 2) A, ] * B R = 1 © 34, x' + 6A,x2 + E [3RA * Σ R = 3 00 E (R - 2) A (a - 2) + 34,]* ЗА R = 1 00 ® 34, x! + 3A, x² + 2 [[R - 2) A (r - 2) + 3 A (R- 2) R = 3 00 © -34, + E [3(r - 2) A ] =* E [3 (R – 2) A,] × (F R = 3

College Algebra
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 10TI: Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+
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Given the power series expression Σ n A x(n + 2) n = 1 3 A x" n = 1 1. Force the first power series to have a simple exponent. 2. Make sure that the power series start at the same value for n. 3. Combine the two power series together into a single power series. A 3 RA x* R = 1 00 © ( - 2) A," B R = 1 3A, x + 6A,x² + RA R = 3 00 D O (R - 2) A (x - 2) + 34] ** (R- 2) R = 1 E 3 A, x' + 3 A, x² + E [(R - 2) A (R - 2) + 3A, R = 3 ® -34, x' + E [3(R – 2) A„ ] ×* F R = 3
Transcribed Image Text:Given the power series expression Σ n A x(n + 2) n = 1 3 A x" n = 1 1. Force the first power series to have a simple exponent. 2. Make sure that the power series start at the same value for n. 3. Combine the two power series together into a single power series. A 3 RA x* R = 1 00 © ( - 2) A," B R = 1 3A, x + 6A,x² + RA R = 3 00 D O (R - 2) A (x - 2) + 34] ** (R- 2) R = 1 E 3 A, x' + 3 A, x² + E [(R - 2) A (R - 2) + 3A, R = 3 ® -34, x' + E [3(R – 2) A„ ] ×* F R = 3
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