Infinite Geometric Series - Idealpedia

This page originally created by Christian and Haowell. (2021)An infinite geometric series is the sum of an infinite geometric sequence. These kinds of series have no last term.General FormFormulaContents1 General Knowledge of the Topic2 Finding the Sum of Infinite Geometric Series3 Expressions in Different Notations4 Good Example Videos5 ReferencesGeneral Knowledge of the Topic[edit] Infinite geometric series can be written in the general expression: a1 + a1r + a1r2 + a1r3 + … + a1r∞, where a1 is the first term and r is the common ratio. The common ratio is a value for which the values in a series gets consistently multiplied by. When the ratio has a magnitude greater than 1, the terms in the sequence will get larger and larger, and if you add larger and larger numbers forever, you will get infinity for an answer. Consider 1⁄2. A sequence might be 1,1⁄2, 1⁄4,1⁄8, 1⁄16, 1⁄32, 1⁄64,1⁄128, 1⁄256, 1⁄512,1⁄1024,1⁄2048, 1⁄4096, 1⁄8192, 1⁄16384, 1⁄32768, 1⁄65536, …. As the sequence goes on, t...