1/2+1/6+1/12+1/20+1/30+1/42 用裂项法
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![1/2+1/6+1/12+1/20+1/30+1/42 用裂项法](/uploads/image/z/3750101-53-1.jpg?t=1%2F2%2B1%2F6%2B1%2F12%2B1%2F20%2B1%2F30%2B1%2F42+%E7%94%A8%E8%A3%82%E9%A1%B9%E6%B3%95)
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1/2+1/6+1/12+1/20+1/30+1/42 用裂项法
1/2+1/6+1/12+1/20+1/30+1/42 用裂项法
1/2+1/6+1/12+1/20+1/30+1/42 用裂项法
1/2+1/6+1/12+1/20+1/30+1/42
=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
=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7
=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
1/2+1/6+1/12+1/20+1/30+1/42
=1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)
=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