1/2=1-1/2,
1/6=1/2-1/3,
1/12=1/3-1/4,
1/20=1/4-1/5.
1/2+1/6+1/12+1/20
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5.
=1-1/5
=4/5
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