Sum to infinity meaning

The sum to infinity of a sequence is the sum of an infinite number of terms in the sequence. It is only possible to compute this sum if the terms of a sequence converge to zero.

1. What is the sum to infinity formula?
2. What is the sum of 1 to infinity?
3. When can you use sum to infinity?

What is the sum to infinity formula?

The general formula for finding the sum of an infinite geometric series is s = ^a₁⁄_1-r, where s is the sum, a₁ is the first term of the series, and r is the common ratio.

What is the sum of 1 to infinity?

For those of you who are unfamiliar with this series, which has come to be known as the Ramanujan Summation after a famous Indian mathematician named Srinivasa Ramanujan, it states that if you add all the natural numbers, that is 1, 2, 3, 4, and so on, all the way to infinity, you will find that it is equal to -1/12.

When can you use sum to infinity?

When Does the Sum to Infinity Exist? The sum to infinity only exists if -1<r<1. If the common ratio is outside of this range, then the series will diverge and the sum to infinity will not exist. If |r|<1, the sequence will converge to the sum to infinity given by S_∞=a/(1-r).