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No. What I would do is find the power series for log(1 + 2x), which is simply a matter of a substitution, and then determine the interval of convergence of the new series.TyErd said:
Mark44 said:
I agree that it's not a difficult problem, but being about series and convergence, it seems a better place for it is in the Calculus & Beyond section.Dick said:
Mark44 said:
Mark44 said:
An interval of convergence is a range of values for which a mathematical series will converge or have a finite sum. In other words, it is the range of values for which the series will not diverge to infinity.
The interval of convergence can be determined by using the ratio test, which compares the absolute value of the terms in the series to the limiting value of the series. If the ratio of the terms is less than 1, the series will converge within a certain range of values.
If the ratio test is inconclusive, other tests such as the root test or the integral test can be used to determine the convergence of the series. If these tests also fail, the series may require more advanced techniques to determine its convergence.
Yes, the interval of convergence can be negative, positive, or a combination of both. It depends on the series and the values of its terms.
Determining the interval of convergence is important because it tells us for which values the series will converge and for which values it will diverge. This allows us to use the series for calculations and understand its behavior.
