Sequences: A sequence is of the form where the are real numbers. Technically,
a sequence is a function whose domain is the set of natural numbers,
and whose range is a subset of the real numbers. Sequences may be
defined in various ways:
By listing, and appealing (via the three dots) to your
intuition. Suppose the sequence is Then
the -th term is
.
Explicitly. For example, suppose . Then
,
, and
.
Recursively. For example, the Fibonacci Sequence is
defined by
Thus
,
, and
.
Also a sequence may or may not have a limit. For the following
sequences, enter the limit, or enter the letter "D" if the sequence
diverges.
.
.
.
You can earn partial credit on this problem.