1/2+1/6+1/12+1/20+1/30、1+5/6-7/12+9/20-11/30
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1/2+1/6+1/12+1/20+1/30
=1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1- 1/6
=5/6
1+5/6-7/12+9/20-11/30
=1+(2+3)/(2×3)-(3+4)/(3×4)+(4+5)/(4×5)-(5+6)/(5×6)
=1+1/2+1/3-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)
=(1+1/2+1/3+1/4+1/5)-(1/3+1/4+1/5+1/6)
=1+1/2-1/6
=4/3
=1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1- 1/6
=5/6
1+5/6-7/12+9/20-11/30
=1+(2+3)/(2×3)-(3+4)/(3×4)+(4+5)/(4×5)-(5+6)/(5×6)
=1+1/2+1/3-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)
=(1+1/2+1/3+1/4+1/5)-(1/3+1/4+1/5+1/6)
=1+1/2-1/6
=4/3
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