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%% https://tex.stackexchange.com/questions/287358/adding-a-star-in-the-tasks-package
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\listfiles
\documentclass{jarticle}
\usepackage{amsmath,tasks,geometry}
\geometry{a4paper, portrait, margin=1in}

\newcommand{\difficult}{%
  \leavevmode\makebox[0pt][r]{\large$\star$\hspace{1.5em}}}

\begin{document}

\begin{enumerate}
  \item Prove the following statements by induction.
  \begin{tasks}(2)
    \task $\displaystyle\sum_{r=1}^n r^5=\frac{n^2}{12}(n+1)^2(2n^2+2n-1)$
    \task\difficult $\displaystyle\sum_{r=1}^n \frac{1}{r(r+1)} = \frac{r}{r+1}$
    \task $\displaystyle\prod_{r=1}^n r^{12}=(r!)^{12}$ 
    \task $\displaystyle\prod_{r=2}^n \biggl( 1-\frac{1}{r^2} \biggr) = \frac{n+1}{2n};~~\forall n\geq 2$
    \task\difficult $\displaystyle\sum_{r=1}^n rx^{r-1} = \frac{1-(n-1)x^n+nx^{n+1}}{(x-1)^2}$
    \task $\displaystyle\sum_{r=1}^n \frac{r^2+r+1}{r(r+1)} = \frac{n(n+2)}{n+1}$
  \end{tasks}
\end{enumerate}

\end{document}
