The Limit of ( (-1)^{n} (n + 100)) / (10n + 3) as n goes to ∞ by Mike Martin
This page allows you to investigate the limit of (-1)^{n} (n + 100) over 10n + 3 as the number of term grows without bound:
To investigate this we consider the sequence whose n^{th} term is given by
The sequence appears to approach a limit, L, as the term number grows without bound and after N terms the sequence value can be within ε units of that supposed 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.
ε = L = y_{min} = y_{max} = n_{min} = n_{max} =