8.5 Infinite geometric series
Unit 8 · Sequences and series
Ideas in this lesson
Test convergence
An infinite geometric series converges exactly when the absolute value of its ratio is less than one.
Find an infinite sum
For a convergent geometric series, divide the first term by one minus the common ratio.
Repeating decimals
Express a repeating block as an infinite geometric series or subtract shifted decimal equations.
Remainders and models
The remaining tail is another geometric series beginning with the first omitted term.
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