Final answer:
The truncation error for S4 is the difference between the actual value of the mathematical expression and its truncated approximation using the first four terms. It is a measure of how closely the truncated approximation approximates the actual value.
Step-by-step explanation:
In mathematics, the truncation error refers to the difference between the actual value of a mathematical expression and its truncated approximation. When we talk about the truncation error for S4, we are referring to the error that occurs when approximating the value of a series using only the first four terms. The truncation error can be calculated by finding the difference between the actual value and the truncated approximation.
For example, let's say we have a series S, and we want to find the value of S using the first four terms, S4. The truncation error for S4 can be calculated as the absolute value of the difference between the actual value of S and the truncated approximation S4.
It's important to note that as we increase the number of terms in the series, the truncation error usually decreases because the approximation becomes more accurate. The truncation error is a measure of how closely the truncated approximation approximates the actual value of the mathematical expression.