Getting back to 1947

Algebra Level 5

If n=0194712n+21947=A22B\sum_{n=0}^{1947}{\frac{1}{2^n + \sqrt{2^{1947}}}} = \frac{A\sqrt{2}}{2^B}

where AA is an odd integer and BB is a positive integer.
What is the value of A+BA + B ?

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