如题所述
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)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=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/(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)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1+(1/2-1/2)+(1/3-1/3)+(1/4-1/4)+(1/5-1/5)-1/6
=1-1/6
=5/6
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第1个回答 2016-06-15
1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
1/30=1/5-1/6
以上各式相加
∴原式=1-1/6=5/6.
1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
1/30=1/5-1/6
以上各式相加
∴原式=1-1/6=5/6.
