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\begin{document}

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\cyr

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\begin{center}{\cyb Analiza 2 (I smer): Stepeni redovi, zadaci za vezhbu} \end{center}


\begin{enumerate}

\item Ispitati obichnu i apsolutnu konvergenciju redova:
%(a)~$\sumn\df{x^{n^2}}{2^n}$; \
\begin{itemize}
\item[(a)]~$\D\suma\(1+\frac 1n\)^{n^2}x^n$;
\item[(b)]~$\D\suma\(1+\frac 12+\dots+\frac 1n\)x^n$;
\item[(v)]~$\D\suma(-1)^n\Bigl[\frac{2^n(n!)^2}{(2n+1)!}\Bigr]x^n$ (bez ispitivanja ponashanja na rubu intervala);
\item[(g)]~$\D\suma\frac{(3+(-1)^n)^n}nx^n$.
%({\dj})~$\suma\(\df x{\sin n}\)^n$.
\end{itemize}
\item Razviti u stepeni red sledec1e funkcije:
\begin{itemize}
\item[a)] $\D f(x)=\sinhyp x$; \
\item[b)] $\D f(x)=\frac x{1+x-2x^2}$; \
\item[v)] $\D f(x)=\sin^3x$; \
\item[g)] $\D f(x)=\ln(1+x+x^2+x^3)$; \
\item[d)] $\D f(x)=\arctg x$; \
\item[dj)] $\D f(x)=\int_0^x\frac{\sin t}t\,dt$; \
%({\dj})~$f(x)=e^x\cos x$; \
\item[e)] $\D f(x)=\ln^2(1-x)$.
\end{itemize}
\item Sabrati sledec1e stepene redove:
\begin{itemize}
\item[(a)]$\D \suma\frac{x^{2n-1}}{2n-1}$;
\item[(b)]$\D \suma(-1)^n\frac{x^{2n}}{n(2n-1)}$;
\item[(v)]$\D \suma nx^n$.
\end{itemize}

\item Sumirati sledec1e redove:
\begin{itemize}
\item[(a)]$\D \suma\frac{2^{2n-1}}{n!}$;
\item[(b)]$\D \suma\frac{(-1)^n+n!}{(2n)!!}$;
\item[(v)]$\D \suma \frac{1}{2^n n}$.
\end{itemize}
\end{enumerate}


\end{document}


