If \[\sum_{n=0}^{1947}{\frac{1}{2^n + \sqrt{2^{1947}}}} = \frac{A\sqrt{2}}{2^B}\]
where \(A\) is an odd integer and \(B\) is a positive integer.
What is the value of \(A + B \)?
by
Agnishom Chattopadhyay
