3.6.08 Series Intro1
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An arithmetic series is the sum of the terms of an arithmetic sequence. There are two ways to find the sum of an arithmetic series: directly adding up all the terms, or using a clever formula developed by Gauss that involves multiplying the average of the first and last terms by the number of terms. This formula allows calculating the sum of large arithmetic series more efficiently than direct addition.
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3.6.08 Series Intro1
- 1. Arithmetic Series A series is similar to a sequence, except that instead of a list of numbers, the numbers are added together. A series is a sum . If is a sequence, then is a finite series. is an infinite series.
- 2. Arithmetic Series An arithmetic series is a the sum of the terms of an arithmetic sequence. There are two ways to find the sum of an arithmetic series: Add everything up. ( duh ) Be clever like Gauss.
- 3. WWGD? In the story about Gauss, he is told to add every integer from 1 to 100… what does he do? +
- 4. We can generalize this approach: +
- 5. Try These: 1. 2. Add up all of the integers from 1 to 500.