An infinite geometric series converges only when |r| < 1 and we can find its sum only if it converges. We know that 'r' represents the common ratio between every two consecutive terms of a geometric series. But if it is infinite, then its sum can be found only when the absolute value of its common ratio is less than 1. If the geometric series is finite, we can find its sum always. Is it possible to Find the Sum of the Geometric Series Always? can be calculated using the formula, Sum of infinite geometric series = a / (1 - r), where a is the first term, r is the common ratio for all the terms and n is the number of terms. The sum formula of an infinite geometric series a + ar + ar 2 + ar 3 +. What is the Infinite Geometric Series Formula? Sum of infinite geometric series = a / (1 - r).These formulas are geometric series with first term 'a' and common ratio 'r' given as, The geometric series formulas are the formulas that help to calculate the sum of a finite geometric sequence, the sum of an infinite geometric series, and the n th term of a geometric sequence. What Are the Geometric Series Formulas in Math? Sum of the given infinite geometric seriesĪnswer: i) Sum = 3280 / 2187 and ii) Sum = 3 / 2įAQs on Geometric Series Formula What is the Difference Between Geometric Series and Geometric Sequence?Ī geometric sequence is the collection of terms where the ratio of every two successive terms is the same whereas a geometric series is the "sum" of the terms of the geometric sequence. Using the sum of the infinite geometric series formula: Ii) The given series is an infinite geometric series. Using the sum of the finite geometric series formula: So we need to find the sum of the first 8 terms of the given series. To find: The sum of the given two geometric series. using the formula for a geometric series. converges when |r| 1 and hence we can't find its sum in this case.An infinite geometric series a, ar, ar 2. But the convergence of an infinite geometric series depends upon the value of its common ratio. Convergence of Geometric SeriesĪ finite geometric series always converges. ![]() To see how this formula is derived, click here.
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