19.3 Infinite Geometric Series

  • Series • Infinity • Limit • Sum of an Infinite Geometric Series • Repeating Decimal

In the previous sections, we developed formulas for the sum of the first n terms of an arithmetic sequence and of a geometric sequence. The indicated sum of the terms of a sequence is called a series.

EXAMPLE 1 Illustrations of series

  1. The indicated sum of the terms of the arithmetic sequence 2, 5, 8, 11, 14, … is the series 2 + 5 + 8 + 11 + 14 +  ⋯ .

  2. The indicated sum of terms of the geometric sequence 1 ,  12 ,  14 ,  18 ,  …  is the series 1 + 12 + 14 + 18 +  ⋯ .

The series associated with a finite sequence will sum up to a real number. The series associated with an infinite arithmetic sequence will not sum up to a real ...

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