Pre-Calculus 12 · Algebra & Patterning
Infinite Geometric Series
An infinite series can have a finite sum — one of mathematics' most surprising ideas. Adding 1/2 + 1/4 + 1/8 + … forever gives exactly 1. The formula S = a/(1−r) applies only when |r| < 1 (the terms shrink to zero). This idea is the conceptual doorstep of calculus, where infinite processes are harnessed to compute areas, lengths, and rates.
WHAT STUDENTS WILL LEARN
✓Determine when an infinite geometric series converges: |r| < 1
✓Calculate the sum of a convergent infinite geometric series: S = a/(1−r)
✓Express repeating decimals as fractions using infinite series
✓Apply convergent series to real-world models
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