![]() Use the formula:, where a = the first term, r = common ratio, and n = number of included terms. Use the formula:, where a = the first term, r = common ratio, and n = number of included terms.Ĥ) Since r = -2, the series diverges. Use the formula:, where a = the first term and r = common ratio.ģ) Since r = 2, the series diverges. Use the formula:, where a = the first term, r = common ratio, and n = number of included terms.Ģ) Since r = 1/5, the series converges. Find the sum of the first 12 terms of the following geometric progression: 2, 4, 8, 16, 32ġ) In finding the sum, identify first if the series converges or diverges.Find the sum of the first nine terms of the geometric sequence whose first term is -25 and the common ratio is 1.5.Identify whether the following series converge or diverge then find the value of the following geometric series. A series that diverges means either the partial sums have no limit or approach infinity. If |r| < 1, then the series will converge. A series that converges has a finite limit, that is a number that is approached. If we multiply the given equation by r both sides,īy subtracting equation 1 from equation 2,ĭepending on the nature of the common ratio, r, a geometric series can converge or diverge. In general, if equal to constant r, the terms are of the form then the geometric sequence is given by: Also, when studying for calculus, you can take the sum of an infinite geometric sequence, but only in the specific condition that the common ratio r is between –1 and 1 that is, you have to have | r | < 1. It is possible to take the sum of a finite number of terms of a geometric sequence. Remember that a geometric sequence has a common ratio. Geometric series is the sum of the terms in a geometric sequence. In higher math, series plays an important role in limits in Calculus.In business, the idea geometric sequence and series is used to represent and predict data.Understanding the concepts behind geometric series is a good foundation in learning about investment growth and loss.FORMULA IN GETTING THE SUM OF GEOMETRIC SERIES.CONVERGENT GEOMETRIC SERIES – A series that converges has a finite limit, that is a number that is approached.GEOMETRIC SERIES – It is the sum of the terms of a geometric sequence.To solve problems involving geometric series such as investment and compound interest.To differentiate convergent and divergent series.To define geometric series and related concepts.Word Problems Involving Geometric Series.
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