Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence. an = n + 3/(n2 + 5n + 6)
Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence. an = n + 3/(n2 + 5n + 6)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.2: Sequences, Series And Summation Notation
Problem 48E
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Question
Which of the sequences {an} converge, and
which diverge? Find the limit of each convergent sequence. an = n + 3/(n2 + 5n + 6)
Expert Solution
Step 1
The given sequence .
We have to check the convergence of the sequence and find its limit if it is convergent.
Step 2
Sequence convergent:
If the sequence of real numbers is convergent, then the limit of the sequence exits finitely.
The given sequence .
Now,
Since the limit exits finitely, the sequence is convergent.
The limit of the sequence is .
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