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SMO 2012 Open Round 1 Question 22

SMO · SMO 2012 Open Round 1

Question 22

Find $\displaystyle\sum_{k=0}^{\infty}\left\lfloor\frac{20121+2^k}{2^{k+1}}\right\rfloor$.

Here $\lfloor x\rfloor$ denotes the greatest integer less than or equal to $x$, as defined in the source paper.