Sum to infinity arithmetic series

The sum of infinite for an arithmetic series is undefined since the sum of terms leads to ±∞. The sum to infinity for a geometric series is also undefined when |r| > 1.

1. How do you find the sum of an arithmetic series to infinity?
2. Why arithmetic does not have sum to infinity?
3. What are the two possible sums of an infinite arithmetic series?

How do you find the sum of an arithmetic series to infinity?

The sum of infinite arithmetic series is either +∞ or - ∞. The sum of the infinite geometric series when the common ratio is <1, then the sum converges to a/(1-r), which is the infinite series formula of an infinite GP. Here a is the first term and r is the common ratio.

Why arithmetic does not have sum to infinity?

Arithmetic series do not converge and so they do not have a defined sum to infinity. If the common difference is positive, then the sum to infinity of an arithmetic series is +∞.

What are the two possible sums of an infinite arithmetic series?

The sum of an infinite arithmetic sequence is either ∞, if d > 0, or - ∞, if d < 0. There are two ways to find the sum of a finite arithmetic sequence.