2011-20 Double infinite series

For a real number x, let d(x)=minn:integer (x-n)2. Evaluate the following double infinite series:
. . . + 8 d(x/8)+4 d(x/4) + 2 d(x/2) + d(x)  + d(2x) / 2 + d(4x)/4 + d(8x)/8 + . . .

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2011-20 Double infinite series, 3.4 out of 5 based on 12 ratings