An infinite series is the sum of the terms of an infinite sequence. It can be represented as S = a_1 + a_2 + a_3 + \ldots , where a_n represents the terms of the sequence. Infinite series can converge, meaning they approach a specific value, or diverge, meaning they do not settle at any particular value. One common example of an infinite series is the geometric series, which has a constant ratio between consecutive terms. The series can be expressed as S = a + ar + ar^2 + ar^3 + \ldots , where a is the first term and r is the common ratio. If the absolute value of r is less than 1, the series converges to \fraca1 - r .