1/1×4+1/4×7+1/7×10+…+1/97×100

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1/1×4+1/4×7+1/7×10+…+1/97×1001/1×4+1/4×7+1/7×10+…+1/97×1001/1×4+1/4×7+1/7×10+…+1/97×100=(1/1-1/4+1/4

1/1×4+1/4×7+1/7×10+…+1/97×100
1/1×4+1/4×7+1/7×10+…+1/97×100

1/1×4+1/4×7+1/7×10+…+1/97×100
=(1/1-1/4+1/4-1/7+1/7-1/10+...+1/97-1/100)/3
=(1-1/100)/3
=0.33

1/1×4+1/4×7+1/7×10+…+1/97×100
=(1/3)*(1-1/4+1/4-1/7+...+1/97-1/100)
=(1/3)*(1-1/100)
=99/300
补充:
1/1*4=(1/3)*(1-1/4)
...

1/1×4=1/3(1/1-1/4)
1/4×7=1/3(1/4-1/7)
.......
1/1×4+1/4×7+1/7×10+…+1/97×100
=1/3(1/1-1/4+1/4-1/7+.......+1/97-1/100)
=1/3*99/100
=33/100

0.33