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Mathematik-Online problems:

Problem 105: Convergence Area of Power Series

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Find the convergence area of the following power series and analyse the behaviour at the boundary:
a) $ f(x) = \displaystyle\sum_{n = 1}^\infty\,x^n$ b) $ f(x) = \displaystyle\sum_{n = 1}^\infty\,\frac{x^n}{n}$ c) $ f(x) = \displaystyle\sum_{n = 1}^\infty\,\frac{x^n}{n^2}$
d) $ f(x) = \displaystyle\sum_{n = 1}^\infty\,2^{n^2} x^{2n + 1}$ e) $ f(x) = \displaystyle\sum_{n = 1}^\infty\,\frac{3^n}{\sqrt{2^n(3n - 2)}}\, (x-1)^n$

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  automatisch erstellt am 29.  7. 2009