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Why does the common ratio in an infinite geometric series have to be between 1 and -1? Why doesn't -2 or 2 work? Please help with this. Thanks in advance!

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Answer:

A n+1 / A n the ratio of successive terms will be less than 1 if A is between -1 and 1 so successive terms will have a ratio less than 1 and can be determined

If A n+1 / A n > 1 then successive values of the given ratio will not approach a constant value

If you write the value of the nth term as L = a r^(n - 1) one can see that r^(n - 1) approaches a fixed value if r between -1 and 1 but not if | r | > 1

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