45+1/8+1/12+1/20+1/30+1/42+1/72+1/90=
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45+1/8+1/12+1/20+1/30+1/42+1/72+1/90

=45+1/8+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(8*9)+1/(9*10)

=45+1/8+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/8-1/9+1/9-1/10

=45+1/8-1/7+1/8+1/3-1/10

=45+143/420

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