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An arithmetic series is the sum of the terms of an arithmetic sequence. If the sequence is finite and short enough, calculating the sum of its terms is quite straightforward.
| Example Arithmetic Sequence | 1, 3, 5, 7, 9 |
|---|---|
| Related Arithmetic Series | 1+ 3+ 5+ 7+ 9=25 |
However, if the sequence is still finite but longer, it can be tedious to add the terms by hand. In that case, the formula for an arithmetic sum can be used. If the arithmetic series is infinite, then the sum is said to diverge. Example Divergent Arithmetic Series ∑_(n=1)^(∞) (3n+1) = 4+7+10+ ... ⇕ ∑_(n=1)^(∞) (3n+1) → ∞