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At the beginning of the task, in order to determine the radius of convergence of the given order, we will use The Ratio Test which says the following:
Let be an arbitrary series such that exists:
Then the following applies:
- (i) If , then the series converges absolutely.
- (ii) If (or is infinite), then the series diverges.
- (iii) If , then the test is inconclusive.
Note: If the powers series is given as
How will we determine ?
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