5/6+5/12+5/20+5/30+5/42+5/56+5/72(简算)

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5/6+5/12+5/20+5/30+5/42+5/56+5/72(简算)

5/6+5/12+5/20+5/30+5/42+5/56+5/72(简算)
5/6+5/12+5/20+5/30+5/42+5/56+5/72(简算)

5/6+5/12+5/20+5/30+5/42+5/56+5/72(简算)
5/6+5/12+5/20+5/30+5/42+5/56+5/72
=5×(1/2-1/3+1/3-1/4+……+1/8-1/9)
=5×(1/2-1/9)
=5×7/18
=35/18

原式=5*(1/6+1/12+1/20+1/30+1/42+1/56+1/72)
=5(1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9)
=5(1/1-1/2+1/2-1/3+.....-1/9)
=5*8/9=40/9