<s>[INST] Proving algebraic operations for this simple problem I cannot wrap my heard around solving this:
$$\mu\frac{1-(\frac{1}{2})^{n+1}}{\frac{1}{2}}=2\mu\left[1-\left(\frac{1}{2}\right)^{n+1}\right]$$
I have done this instead:
\begin{align}
\mu\frac{1-(\frac{1}{2})^{n+1}}{\frac{1}{2}}&=\mu\frac{1}{\frac{1}{2}}-\frac{(\frac{1}{2})^{n}(\frac{1}{2})^{1}}{\frac{1}{2}}\\
&=2\mu-\frac{1}{2}^{n}
\end{align}
What have I done wrong?
 [/INST] thanks guys!
What about this one
\begin{align}
\mu\frac{1-(\frac{1}{4})^{n+1}}{\frac{3}{4}}&=\mu\frac{1}{\frac{3}{4}}-\frac{(\frac{1}{4})^{n}(\frac{1}{4})^{1}}{\frac{3}{4}}\\
\end{align}
I don't know how to proceed from this other than 
\begin{align} \frac{4}{3}\mu-\mu(\frac{3}{4})^{n+1} \end{align}
which is obviosly wrong. As the result should be 
\begin{align} \frac{4}{3}\mu[1-(\frac{1}{4})^{n+1}] \end{align}
Thanks
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