Chapter 7.4, Problem 1E

Solution

To Fill in : The blank for the sum $S_n$ of the first $n$ terms of an infinite series is called $a\left(n\right)$ ____.

The sum $S_n$ of the first $n$ terms of an infinite series is called $a\left(n\right)$partial sum.

Given information :

The sum $S_n$ of the first $n$ terms of an infinite series $a\left(n\right)$ .

Explanation :

Consider the first $n$ terms of an infinite series $a\left(n\right)$ ,

In the infinite series, if the sum of the finite number of the consecutive terms is taken in which the first term is also includes, then the sum of those numbers is called a partial sum of the series.

The partial sum of an infinite series might approach to any limiting value.

Thus, the sum $S_n$ of the first $n$ terms of an infinite series is called $a\left(n\right)$partial sum.