1/20+1/30+1/42+……+1/132
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1/20+1/30+1/42+……+1/1321/20+1/30+1/42+……+1/1321/20+1/30+1/42+……+1/132注意观察,20=4*5,30=5*6,42=6*7……132=
1/20+1/30+1/42+……+1/132
1/20+1/30+1/42+……+1/132
1/20+1/30+1/42+……+1/132
注意观察,20=4*5,30=5*6,42=6*7……132=11*12
1/(4*5)=1/4-1/5,1/(5*6)=1/5-1/6……
题目条件可整理成:1/(4*5)+1/(5*6)+1/(6*7)+……+1/(11*12)
=1/4-1/5+1/5-1/6+1/6-1/7+……+1/10-1/11+1/11-1/12
=1/4-1/12
=1/6
1/20+1/30+1/42+……+1/132
=1/(4*5)+1/(5*6)+……+1/(11*12)
=(1/4-1/5)+(1/5-1/6)+……+(1/11-1/12)
=1/4-1/12=1/6
1/4-1/12=1/6
=(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)+(1/10-1/11)+(1/11-1/12)=1/4-1/12=1/6 =0.1666666....
原式=(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+……+(1/11-1/12)
=1/4-1/5+1/5-1/6+1/6-1/7+……+1/11-1/12
=1/4-1/12
=1/6