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%  Testing Series with Positive Terms              %
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\problemgrouptitle{Testing Series with Positive Terms}

\begin{problemblock}[2]{Determine whether the infinite series is convergent or divergent.}

\addtoanswerkey{\begin{multicols}{2}}
  
\item $\displaystyle \sum_{n=1}^{\infty} \frac{\ln(n+1)}{n+1}$
\answer{
divergent
}

\item $\displaystyle \sum_{n=1}^{\infty} \frac{5}{2+3n^2}$
\answer{
convergent
}

\item $\displaystyle \sum_{n=1}^{\infty} \frac{1}{n \sqrt[5]{\ln n}}$
\answer{
divergent
}

\item $\displaystyle \sum_{n=1}^{\infty} \frac{2n^2+5n}{5n^3+3}$
\answer{
divergent
}

\item $\displaystyle \sum_{n=1}^{\infty} \frac{1}{\sqrt{9n^4+5n}}$
\answer{
convergent
}

\item $\displaystyle \sum_{n=1}^{\infty} \frac{\ln n}{n^6}$
\answer{
convergent
}

\item $\displaystyle \sum_{n=1}^{\infty} \frac{2+4^n}{3+5^n}$
\answer{
convergent
}

\item $\displaystyle \sum_{n=1}^{\infty} \frac{1}{\sqrt[4]{2n^3+5}}$
\answer{
divergent
}

\item $\displaystyle \sum_{n=1}^{\infty} \frac{5+\cos 2n}{n^3}$
\answer{
convergent
}

\item $\displaystyle \sum_{n=1}^{\infty} \frac{1}{\sqrt{n(n+5)}}$
\answer{
divergent
}

\addtoanswerkey{\end{multicols}}

\end{problemblock}

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