计算 1/2+ 1/6+ 1/12+ 1/20+1/30 +1/42 的值.( )

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计算1/2+1/6+1/12+1/20+1/30+1/42的值.()计算1/2+1/6+1/12+1/20+1/30+1/42的值.()计算1/2+1/6+1/12+1/20+1/30+1/42的值.

计算 1/2+ 1/6+ 1/12+ 1/20+1/30 +1/42 的值.( )
计算 1/2+ 1/6+ 1/12+ 1/20+1/30 +1/42 的值.( )

计算 1/2+ 1/6+ 1/12+ 1/20+1/30 +1/42 的值.( )
1/2+ 1/6+ 1/12+ 1/20+1/30 +1/42
=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)
=1-1/2+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)+(1/2-1/3)+(1/3-1/4)+...+(1/6-1/7)=1-1/7=6/7

1/2+1/6+...+1/42
=1/1*2+1/2*3+1/3*4+....+1/6*7
=1-1/2+1/2-1/3+1/3-1/4+...+1/6-1/7
=1-1/7
=6/7

6/7