Show that,
\[
\begin{array}{r}
\left(1+5^{-1}\right)\left(1+5^{-2}\...
Show that,
\[
\begin{array}{r}
\left(1+5^{-1}\right)\left(1+5^{-2}\right)\left(1+5^{-4}\right)\left(1+5^{-8}\right) \ldots\left(1+5^{-2^{n}}\right) \\
=\frac{5}{4}\left(1-5^{-2^{n+1}}\right)
\end{array}
\]
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