Remainder term

Definition

The remainder term, also known as error or residual term, represents how close our approximation using a truncated version of the Taylor series is to the actual value of the function. It quantifies how much we've left out by stopping at a certain number of terms in our approximation.

Related terms

Truncated Taylor Series: An approximation obtained by taking only up to a certain number (n) terms in a Taylor Series.

Order of approximation: The highest degree term included in our truncated Taylor Series; determines how many terms are used in the approximation.

Convergence:

The behavior of a series where it approaches a specific value as more terms are added; if a series converges, the remainder term tends to zero.