Section 10.1
Sequences
A sequence is a function whose domain is the integers. Does the list of numbers settle down to a single value (limit) or wander forever?
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Limit of a Sequence
.
If the limit exists, the sequence Converges. Otherwise, it Diverges.
Sequence Plotter
a_n = n / (n+1)
n = 20
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Worked Examples
1. Rational Sequence
Find limit of .
Strategy
Divide numerator and denominator by highest power ().Result
.Converges.
2. Alternating Sequence
Determine convergence of .
Analysis
Terms: The magnitude approaches 1, but the sign flips back and forth forever.
Result
It never settles on a single number.Diverges.
3. Geometric Sequence
Determine convergence of .
Theory
geometric sequences converge if .Result
Since base , limit is 0.Converges.
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Practice Quiz
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