## Related questions with answers

Question

Why must the absolute value of the common ratio be less than 1 before an infinite geometric sequence can have a sum?

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Notice that if a common ratio of an infinite geometric sequence is greater than $1$, then the terms will get larger and larger which leaves a sum of infinity. However, if the common ratio is less than $1$, the terms will get smaller and smaller which leaves a specific sum.

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