MathDB
Show that [√(4n + 2)] = [√(4n + 3)] = [√n + √(n + 1)]

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October 3, 2011

Problem Statement

For every positive integer nn show that [4n+1]=[4n+2]=[4n+3]=[n+n+1][\sqrt{4n + 1}] = [\sqrt{4n + 2}] = [\sqrt{4n + 3}] = [\sqrt{n} + \sqrt{n + 1}] where [x][x] is the greatest integer less than or equal to xx (for example [2.3]=2[2.3] = 2, [π]=3[\pi] = 3, [5]=5[5] = 5).
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