Geometric Series in Geometry
The sum of the lengths of line segments or areas in figures that endlessly repeat with similar shapes can be found using geometric series:
Use the repeating property to find the first term and the common ratio .
Calculate the sum of the geometric series using the formula .
Repeating Decimals and Geometric Series
Express the repeating decimal as a geometric series.
Identify the first term and the common ratio .
Find the sum of the geometric series using the formula .
Example.For the geometric sequence with the first term and common ratio , given , find the value of the single-digit natural number .