1/1乘4+1/4乘7+1/7乘10+.1/97乘100,得多少

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1/1乘4+1/4乘7+1/7乘10+.1/97乘100,得多少
1/1乘4+1/4乘7+1/7乘10+.1/97乘100,得多少

1/1乘4+1/4乘7+1/7乘10+.1/97乘100,得多少
1/1×4+1/4×7+1/7×10+...+1/97×100
=(1/3)×(3/1×4+3/4×7+3/7×10+...+3/97×100)
=(1/3)×[(1-1/4)+(1/4-1/7)+(1/7-1/10)+...+(1/97-1/100)]
=(1/3)×(1-1/4+1/4-1/7+1/7-1/10+...+1/97-1/100)
=(1/3)×(1-1/100)
=(1/3)×(99/100)
=33/100

先提出3分之1
=1/3*(1-1/4+1/4-1/7`````+1/97-1/100)
=1/3*(1-1/100)
=33/100