integration of ((|x|)/([x]) from (1,9)..

throughout the range of x, mod(x)=x, I=∫(x/[x])dx from 1 to 9, =∫(x/[x])dx from 1 to 2...from 8 to 9

∑(((i+1)²-i²)/2)/i    from i=1 to i=8

=3/2 + 5/4 +7/6 +9/8 = 121/24

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