# 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?

• Sum to $n$ terms of the series: $$\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + \cdots$$
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Hint: The $k$th term is $1-\frac1{2^k}$. –  Did Jun 3 '12 at 15:39

Write it as $(1-{1\over2})+(1-{1\over4})+(1-{1\over 8})+\cdots+(1-{1\over 2^n}).$