MathDB
2014 Team #4: Sum Involving the Floor Function

Source:

March 2, 2014
functionfloor function

Problem Statement

Compute ∑k=0100⌊2100250+2k⌋.\sum_{k=0}^{100}\left\lfloor\dfrac{2^{100}}{2^{50}+2^k}\right\rfloor. (Here, if xx is a real number, then ⌊x⌋\lfloor x\rfloor denotes the largest integer less than or equal to xx.)
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