Educator

Infinite Geometric Series

• Remember that an infinite geometric series converges only if |r| < 1. If you are given a series to evaluate, first check the value of r. If it does not satisfy this condition, the series does not have a sum.

• To convert a repeating decimal to a fraction, let r = 10^-n , where n = number of digits in the repeating pattern of the decimal. Let a₁ = the fraction which contains the pattern written once in the numerator and 10ⁿ in the denominator.