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Convergence and Divergence.
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Sequences of real numbers.
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Geometric sequences.
Contents
Monotonous sequences.
Definition
3
.
5
.
1
Let
be a sequence of real numbers.
The sequence
is constant if
.
The sequence
increases if
.
The sequence
decreases if
.
The sequence
is monotonous if it is either decreasing or increasing.
Example
3
.
5
.
2
An arithmetic sequence whose difference is positive is an increasing sequence.
An arithmetic sequence whose difference is negative is a decreasing sequence.
A geometric sequence whose quotient is greater than 1 and whose first term is positive is an increasing sequence.
A geometric sequence whose quotient is negative is not monotonous.
The sequence whose general term is equal to
is an increasing sequence.
The number of atoms of Uranium 235 present in an atomic pile, checked every minute, define a decreasing sequence.
Noah Dana-Picard 2007-12-28