(b) Under what conditions does an alternating series converge? An alternating series E an = (-1)" - 'bn, where bn = lanl, converges if 0 < bn + 1 < bn for all n, and lim b, = n- 00 n = 1 n = 1

College Algebra
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ISBN:9781938168383
Author:Jay Abramson
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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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 Under what conditions does an alternating series converge?

(b) Under what conditions does an alternating series converge?
lim bn
00
and
2 (-1)" - 'bn, where bn = |anl, converges if 0 < bn + 1 < bn for all n,
n → 00
An alternating series >
an
n = 1
n = 1
Transcribed Image Text:(b) Under what conditions does an alternating series converge? lim bn 00 and 2 (-1)" - 'bn, where bn = |anl, converges if 0 < bn + 1 < bn for all n, n → 00 An alternating series > an n = 1 n = 1
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