Our definition of convergence for an infinite sequence may look like the definition of a limit for functions.
|Theorem: Relation to Limits of Functions
If we have that
and f(n) = an, where x is a real number and n is an integer, then
The above theorem makes it easier for us to evaluate limits of sequences.
Suppose we wish to determine whether the sequence
converges, where p is any positive integer.
Since we know that
for any integer p greater than zero, our theorem yields
Therefore, the given sequence