Determine the sums of the following geometric series when they are convergent. 1-(1)/(3^2)+(1)/(

step 1 In this question, we're finding the sum of a geometric series. In order to do that, we need to u

Determine the sums of the following geometric series when...

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Key Concepts

Sum of an Infinite Geometric Series

For a convergent infinite geometric series, the sum can be calculated using the formula S = a / (1 - r), where a is the first term and r is the common ratio. This formula simplifies the process of finding the total sum of all terms in the series.

Convergence of Infinite Series

An infinite geometric series converges if the absolute value of the common ratio is less than one. This convergence criterion ensures that the terms of the series diminish sufficiently fast, allowing the series to approach a finite limit.

Common Ratio

The common ratio is the fixed multiplier between successive terms in a geometric series. Its magnitude determines whether the series converges or diverges, with |r| < 1 being the condition for convergence in an infinite series.

Geometric Series

A geometric series is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant factor. This constant factor is called the common ratio and it dictates the behavior and properties of the series.

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