Getting back to 1947

Algebra Level 5

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 \(A + B \)?

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