For what values of x does the series 1 + 3x + 9x^2 + 27x^3 + ... converge

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For what values of x does the series 1 + 3x + 9x^2 + 27x^3 + ... converge

[From: ] [author: ] [Date: 12-05-10] [Hit: ]

Justify your answer with both mathematical work and a brief explanation in words.

This is a geometric series with r = 3x.
So, this converges when |r| = |3x| < 1 <==> |x| < 1/3.

I hope this helps!

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