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I've no clue where to start from. I tried writing down a few terms to find out a pattern but didn't notice any. Any help would be appreciated! :)

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  • $\begingroup$ $$\frac{1}{2^n + \sqrt{2^{1947}}} + \frac{1}{2^{1947-n} + \sqrt{2^{1947}}} =\;?$$ $\endgroup$ – achille hui Nov 2 '14 at 15:59
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    $\begingroup$ $$\frac{1}{2^n + \sqrt{2^{1947}}} + \frac{1}{2^{1947-n} + \sqrt{2^{1947}}} = \frac{\sqrt{2^{1947}}}{\sqrt{2^{1947}}(2^n + \sqrt{2^{1947}})} + \frac{2^n}{\sqrt{2^{1947}}^2 + 2^n\sqrt{2^{1947}}}\\ = \frac{\sqrt{2^{1947}}}{\sqrt{2^{1947}}(2^n + \sqrt{2^{1947}})} + \frac{2^n}{\sqrt{2^{1947}}(\sqrt{2^{1947}} + 2^n)} = \frac{1}{\sqrt{2^{1947}}} $$ Is that obvious now? $\endgroup$ – achille hui Nov 2 '14 at 16:11

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