Question

Define the following. A. Sum of a series using the sequence of partial sums.

Answer 1

In mathematics, the sum of a series using the sequence of partial sums refers to the sum of all the terms in a series by adding up the partial sums. The partial sums of a series are obtained by adding up a certain number of terms from the series. As more terms are added, the partial sums converge to the sum of the entire series.

Step-by-step explanation:

In mathematics, the sum of a series using the sequence of partial sums refers to the sum of all the terms in a series by adding up the partial sums. The partial sums of a series are obtained by adding up a certain number of terms from the series. As more terms are added, the partial sums converge to the sum of the entire series.

Example:

Consider the series 1 + 2 + 3 + 4 + ...

The sequence of partial sums would be:

1. Partial sum after 1 term: 1
2. Partial sum after 2 terms: 1 + 2 = 3
3. Partial sum after 3 terms: 1 + 2 + 3 = 6
4. Partial sum after 4 terms: 1 + 2 + 3 + 4 = 10

The sum of the series using the sequence of partial sums would be the limit of the partial sums as the number of terms approaches infinity. In this case, the sum of the series would be infinity since the series diverges.