LimitsAndContinuity

# limit of a sequence

The sequence is said to **converge** if there exists a number *L* such that no matter how close we want the a_{n} to be to *L*, we can find a natural number k such that all terms {a_{k}, a_{k+1}, ...} are as close to *L*.

Then it is said that the sequence is **convergent** and *L* is its limit,

Otherwise, it is said that the sequence is **divergent**.

Examples:

· is convergent and

· diverges and

· is an oscillating sequence and does not exist

Properties:

Note:

Examples:

**Exercise**: calculate:

Solutions: a) -∞; b) 1; c) 0

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