Which of the series E=1a, defined by the formulas in Exercises 5–8 converge, and which diverge? Give reasons for your answers. n(n + 1) 5. а, — 1, ал+1 (n + 2)(n + 3)ªn (Hint: Write out several terms, see which factors cancel, and then generalize.) п 6. ај — аз —D 7, а,+1 (n – 1)(n + 1)' a, if n > 2 7. a¡ = a2 = 1, a„+1 = if n 2 2 1 + an 8. a, = 1/3" if n is odd, a, = n/3" if n is even

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
Which of the series E=1a, defined by the formulas in Exercises 5–8
converge, and which diverge? Give reasons for your answers.
n(n + 1)
5. а, — 1, ал+1
(n + 2)(n + 3)ªn
(Hint: Write out several terms, see which factors cancel, and then
generalize.)
п
6. ај — аз —D 7, а,+1
(n – 1)(n + 1)'
a, if n > 2
7. a¡ = a2 = 1, a„+1 =
if n 2 2
1 + an
8. a, = 1/3" if n is odd, a, = n/3" if n is even
Transcribed Image Text:Which of the series E=1a, defined by the formulas in Exercises 5–8 converge, and which diverge? Give reasons for your answers. n(n + 1) 5. а, — 1, ал+1 (n + 2)(n + 3)ªn (Hint: Write out several terms, see which factors cancel, and then generalize.) п 6. ај — аз —D 7, а,+1 (n – 1)(n + 1)' a, if n > 2 7. a¡ = a2 = 1, a„+1 = if n 2 2 1 + an 8. a, = 1/3" if n is odd, a, = n/3" if n is even
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