I keep getting “Infinite geometric series” questions wrong in Sequences & Series. What's the trap?
applying the sum formula when |r| ≥ 1.
The usual trap: applying the sum formula when |r| ≥ 1. How to avoid it: if the terms don't shrink (|r|≥1), the series diverges — no finite sum. Go back to the definition — an infinite GP has a finite sum a/(1−r) only when |r| < 1.
Key point
Infinite geometric series
Common mistake
applying the sum formula when |r| ≥ 1.
Memory tip
if the terms don't shrink (|r|≥1), the series diverges — no finite sum.
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