# find the interval of absolute convergence for the given power series `sum_{n=0}^infty (3x)^n`

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This is a geometric series like `sum_{n=0}^infty z^n` , which converges provided `|z|<1` .

In this case, this means that the series converges provided `|3x|<1` which is equivalent to `|x|<1/3` .

**Therefore the interval of absolute convergence is `(-1/3,1/3)` .**

**Sources:**