1/2+1/6+1/12+1/20+1/30+1/42=6/7
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= 1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7
= 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
= 1-1/7
= 6/7
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1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42
= 2/3 + 1/12 + 1/20 + 1/30 + 1/42
= 3/4 + 1/20 + 1/30 + 1/42
= 4/5 + 1/30 + 1/42
= 5/6 + 1/42 = 6/7
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1/2+1/6+1/12+1/30+1/42
=1/2+1/(2.3)+1/(3.4)+1/(4.5)+1/(5.6)+1/(6.7)
=1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1/2+1/2-1/7
=1-1/7
=7/7-1/7
=6/7
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