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4. Do the following task. a. State formally the definition of infinite series C. terms of the limit of partial sum. n=1 State formally when the infinite series ¡Σª an in R converge in an in R. n=1 Show that the series (-1)"-¹ = 1 − 1 + 1 - 1 + 1 - 1 + ....

4. Do the following task. a. State formally the definition of infinite series C. terms of the limit of partial sum. n=1 State formally when the infinite series ¡Σª an in R converge in an in R. n=1 Show that the series (-1)"-¹ = 1 − 1 + 1 - 1 + 1 - 1 + ....

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. Do the following task. a. State formally the definition of infinite series ex an in R. C. terms of the limit of partial sum. State formally when the infinite series ¡Σª an in R converge in Am1 n=1 Show that the series (-1)"-1 = 1−1+1−1+1−1+... n=1 1 diverge by showing that the limit of the partial sum s,,= 1-1+...+(-1)"-1 does not exists. Hint: Consider the subsequence ($2,) and {$2n-1) of the sequence {sn}.
Transcribed Image Text:4. Do the following task. a. State formally the definition of infinite series ex an in R. C. terms of the limit of partial sum. State formally when the infinite series ¡Σª an in R converge in Am1 n=1 Show that the series (-1)"-1 = 1−1+1−1+1−1+... n=1 1 diverge by showing that the limit of the partial sum s,,= 1-1+...+(-1)"-1 does not exists. Hint: Consider the subsequence ($2,) and {$2n-1) of the sequence {sn}.
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