![]() If the common ratio is outside of this range, then the series will diverge and the sum to infinity will not exist. The sum to infinity only exists if -1 ![]() The first term is simply the first number in the series, which is 1. It does not matter which term you choose, simply divide any term by the term before it to find the value of r.įor example, the same result is obtained by considering the last two terms instead. We can divide the term by the term before it, which is 1. Calculate r by dividing any term by the previous term Calculate the sum to infinity with S â = a 1 ÷ (1-r).įor example, find the sum to infinity of the series.Calculate r by dividing any term by the previous term.To find the sum to infinity of a geometric series: The sum to infinity of a geometric series ârâ is the common ratio between each term in the series.The sum to infinity of a geometric series is given by the formula S â=a 1/(1-r), where a 1 is the first term in the series and r is found by dividing any term by the term immediately before it. How to Find the Sum to Infinity of a Geometric Series This means that the sequence sum will approach a value of 8 but never quite get there. ![]() The sum of an infinite number of terms of this series is 8. The sum to infinity of the series is calculated by, where is the first term and r is the ratio between each term.įor this series, where and, which becomes. We can see that the sum is approaching 8.Ä®ventually, if an infinite number of terms could be added, the sum would indeed approach 8. Ä«ecause the terms are getting smaller and smaller, as we add more terms, we are adding an increasingly negligible amount. As more terms are added, we see that, , and.
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