<s>[INST] 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: $$ \frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + \cdots$$
  

 [/INST] Hint:
Write it as $(1-{1\over2})+(1-{1\over4})+(1-{1\over 8})+\cdots+(1-{1\over 2^n}).$
</s>