数学题在线解答1/2+1/6+1/12+1/20+1/30+1/42+1/56=
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1/2+1/6+1/12+1/20+1/30+1/42+1/56=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+1/7-1/8=1-1/8=7/8
1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/7-1/8=1-1/8=7/8
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=1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8=7/8
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1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+/1(7*8)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)
=1-1/8
=7/8
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+/1(7*8)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)
=1-1/8
=7/8
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用裂项做。
1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/2+1/(2*3)+1/(3*4)+...+1/(7*8)
=1/2+1/2-1/3+1/3-1/4+1/4-1/5.....-1/8
=1-1/8=7/8
1/2+1/6+1/12+1/20+1/30+1/42+1/56
=1/2+1/(2*3)+1/(3*4)+...+1/(7*8)
=1/2+1/2-1/3+1/3-1/4+1/4-1/5.....-1/8
=1-1/8=7/8
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