What Is the Infinite Series Sum?

# What Is the Infinite Series Sum?

The infinite series sum usually deals with geometric series. The sum of an infinite geometric series, denoted as "S", is t1 / (1 - r), where "t1" is the first term of the series and "r" is the common ratio between the numbers in the series.

A geometric series may continue to infinity if there are no limits defined. However, this does not necessarily mean that the sum of the infinite series is equal to infinity. There is a need to identify the convergence of the series, which is the characteristic of a given series to approach a given finite number. A geometric series may be either convergent or divergent. A series is denoted as convergent if the terms approach a given number as the number of iterations approaches infinity. On the other hand, a divergent series does not approach a specific finite number as the number of repetitions approaches infinity. In other words, the sum of an infinite divergent series is equal to infinity.

The behavior of each term of an infinite convergent series tends to decrease until it approaches a specific number, usually zero. The limit of the series is denoted by the sum of the said infinite series, which can be calculated using the formula S = t1 / (1 - r). The common ratio is determined by dividing the second term by the first term. The value of "S" should always be positive and finite for it to be considered a limiting sum of the infinite series.

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