Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence. $sum (9x)^k$ The radius of convergence is R =
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First, we need to use the ratio test to determine the radius of convergence: |e^(rx[k+1])/e^(rx[k])| = |e^(rx)| Since this expression does not depend on k, we can simplify it to: |e^(rx)| < 1 Taking the natural logarithm of both sides, we get: rx < 0 or r < Show more…
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