The Limit of a Sequence as n goes to ∞
by Mike Martin

This page allows you to investigate the limit of a sequence as the number of term grows without bound:

To investigate this we consider the sequence whose nth term is given by

The sequence may approach a limit, L, as the term number grows without bound and after N terms the sequence value is known to be within ε units of that limiting value. This tool is designed for you to investigate the relationship between the number of terms in the sequence and ε, placing it in context with the definition of the limit of a sequence. The value of the last term calculated is printed at the top of the graph and it is accurate to 16 decimal places.

Enter the value of the parameters below, then press Evaluate.

ε =

ymin =

ymax =

nmin =

nmax =