# Formal Limit of a Sequence

## Limit of Sequence

A sequence is a function whose domain is the natural numbers. We use for the output of the sequence instead of a(k). The graph of the sequence consists of isolated dots with natural number first coordinates. We say that the infinite sequence converges to a limit L if and only if for every positive number epsilon () there exists a positive number M such that if k > M then . This formal definition is illustrated in the app above. Enter a formula for the sequence in the input box using k as the independent variable. Enter the value of its limit in the input box for L. Choose a value for epsilon. Manipulate M by moving point M on the x-axis. If the choice of limit is correct, then you should be able to choose a value for M so that to the right of M the sequence always stays inside the shaded region, regardless of how small a value is chosen for epsilon.