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\problemgrouptitle{Power Series}

\begin{problemblock}{Find the interval and the radius of convergence of the power series.}

\item $\displaystyle \sum_{n=0}^{\infty}  \frac{n^2+4}{2n^3+5} x^n$
\answer{
$\displaystyle  I=[-1, 1),\   R=1$
}

\item $\displaystyle \sum_{n=2}^{\infty}   \frac {\ln n}{n^2} (x-1)^n$
\answer{
$\displaystyle  I=[0, 2],\   R=1$
}

\item $\displaystyle \sum_{n=0}^{\infty}   \frac{3^n}{(3n)!}   x^{3n}$
\answer{
$\displaystyle   I=(- \infty, \infty ),\   R=\infty$
}

\item $\displaystyle \sum_{n=1}^{\infty}(-1)^{n} \frac{1}{n  3^n}  (4x-1)^{n}$
\answer{
$\displaystyle I=\left(- \frac 12, 1 \right) ,\   R=\frac 34$
}

\item $\displaystyle \sum_{n=0}^{\infty} \frac{n!}{10^n}   (x-1)^n$
\answer{
$\displaystyle  I=\{1\},\  R=0$
}

\end{problemblock}

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