is there a formula for an INFINITE ARITHMETIC series/sequence?
i know its not s = a / 1-r.. that's for geometric.
An infinite arithmetic series will have the same number added or subtracted an infinite number of times, so the last term must become infinite in the limit
Yes, there is a formula for the sum of an infinite arithmetic series. The formula is given by:
S = a / (1 - r)
In this formula:
- S represents the sum of the series
- a represents the first term of the series
- r represents the common difference between successive terms
However, it is important to note that this formula is applicable only if the common difference (r) lies between -1 and 1, making the series convergent. If the common difference is outside this range, the series diverges and does not have a finite sum.
Yes, there is a formula to find the sum of an infinite arithmetic series. Unlike the finite arithmetic series, where there is a fixed number of terms, the infinite arithmetic series continues indefinitely.
The sum of an infinite arithmetic series can be calculated using the formula:
S = a / (1 - d),
where:
S is the sum of the series,
a is the first term of the series, and
d is the common difference between consecutive terms.
It's important to note that this formula for the sum of an infinite arithmetic series is only applicable when the common difference (d) is between -1 and 1. If the common difference is outside this range, the series diverges and does not have a sum.
To use this formula, you need to know the value of the first term (a) and the common difference (d). Simply substitute these values into the formula, and you will get the sum (S) of the infinite arithmetic series.