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`sum_(n=0)^oo (x/k)^n , k>0` Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.)

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This is a geometric series, which will converge if and only if `|x| < k`. It must be strictly less, as the series `(-1)^n and `(1)^n` do not converge.

Therefore the interval of convergence is just this:
`-k < x < k`

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