Determine whether each of the following series (Sum from 1 to infinity) are absolutely convergent, conditionally convergent, or divergent. i. ∑ (-2)n2 / (n + 2)! ii. ∑ (-3)n / (3n2 + 6n) iii. ∑ (-4)n / ( 4n⋅√2n +1 )

Determine whether each of the following series (Sum from 1 to infinity) are absolutely convergent, conditionally convergent, or divergent. i. ∑ (-2)n2 / (n + 2)! ii. ∑ (-3)n / (3n2 + 6n) iii. ∑ (-4)n / ( 4n⋅√2n +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 10TI: Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+

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Question

Determine whether each of the following series (Sum from 1 to infinity) are absolutely convergent, conditionally convergent, or divergent.
i. ∑ (-2)ⁿ² / (n + 2)!
ii. ∑ (-3)ⁿ / (3n² + 6ⁿ)
iii. ∑ (-4)ⁿ / ( 4ⁿ⋅√2n +1 )