Summation of $ \frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + \cdots$ till $n$ terms What is the pattern in the following?

  
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*Sum to $n$ terms of the series: $$ \frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + \cdots$$
  


Here is the pattern:
\begin{align*}
\frac{1}{2} + \frac{3}{4} + \cdots &= \biggl(1-\frac{1}{2}\biggr) + \biggl(1-\frac{1}{2^2}\biggr) + \cdots \\\ &= (1+1+\cdots + 1) - \biggl(\frac{1}{2}+\frac{1}{2^2} + \cdots +\frac{1}{2^n}\biggr)
\end{align*}
