8-2 Limits of Sequences

1
8-2Limitsof Sequences
2
Limits

• Limits ask what the value of a function goes
  towards as the independent variable approaches a
  certain number.
• Divergent Sequence Sequences that increase (or
  decrease) to no finite limit. (Infinity or
  negative infinity)
• Convergent Sequence Sequences which have a
  finite numerical limit.

3
Example 1

• Generate a few terms and graph the following 2
  sequences.
• an -2n
• bn n2
• Do you think these are divergent or convergent
  sequences?
• What about tn ?
• How about sn ?

4
Limit Notation

• Read as
• The Limit
• of (1 1/n)n
• as n approaches infinity

5
The Harmonic Sequence

• Harmonic sequence The sequence of reciprocals
  of positive integers.
• Limit Property
• Alternating Harmonic Sequence

These sequences are Convergent because they
approach a finite numerical value.
0
6
Limit Properties
7
Limit Properties
Or, this property pertains to any fraction where
the degree in the denominator is more than the
degree in the numerator.
8
Application of Properties

• Find the limits of the following, if they exist

This is a problem Parts of the sequence
converge, and parts diverge.
First you must divide ALL Parts of the
sequence by the variable to the highest degree in
the sequence. In this case n2
Divergent