Denis99
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Find Radius and Interval of Convergence for $$\sum_{1}^{\infty}(\frac{x}{sinn})^{n}$$.
I don`t have any ideas how to do that :/
I don`t have any ideas how to do that :/
Country Boy said:The standard method of determining the radius of convergence of power series is to use the "ratio test": \left|\left(\frac{x^{n+1}}{sin^{n+1}(n+1)}\right)\left(\frac{sin^n(n)}{x^n}\right)\right|= |x|\frac{sin^n(n)}{sin^{n+1}(n+1)}.
The radius of convergence is 1 over the limit of the fraction.
The ratio test won't work in this example. I think you will find that in this case the radius of convergence is zero. To see that, use the "$n$th term test": if the $n$th term of a series does not tend to zero then the series does not converge.Denis99 said:Find Radius and Interval of Convergence for $$\sum_{1}^{\infty}(\frac{x}{sinn})^{n}$$.
I don't have any ideas how to do that :/