finding error when truncating a series
Because we can't actually add or evaluate an infinite amount of terms (which what sequences and series should do in theory), must truncate, or cut off, the series at a point. In doing so, we'd like to know the maximum amount of error created. The remainder or error found is also called the Lagrange form and the bounds found are called the Lagrange error bounds.
Below is the formula used to find the error.
Below is the formula used to find the error.
Wondering About m?
This value is not an actual number (well it is), but should be thought of as an upper bound used to maximize the potential error. It is refered to as M.