Question

简算:1/1*4+1/4*7+1/7*10+...+1/100*103

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Answer 1

1/100*103=1/3[(1/100)-(1/103)]

代入，1/1*4+1/4*7+1/7*10+...+1/100*103
=1/3(1-1/4+1/4-1/7+……+1/100-1/103）
=1/3*(1-1/103)
=34/103

Answer 2

1/1×4+1/4×7+1/7×10+...+1/100×103

=(1/3)×(3/1×4+3/4×7+3/7×10+...+3/100×103)

=(1/3)×[(1-1/4)+(1/4-1/7)+(1/7-1/10)+...+(1/100-1/103)]

=(1/3)×(1-1/4+1/4-1/7+1/7-1/10+...+1/100-1/103)

=(1/3)×(1-1/103)

=(1/3)×(102/103)

=34/103

Answer 3

1/4=(1-1/4)/3,1/4*7=(1/4-1/7)/3
1/1*4+1/4*7+1/7*10+...+1/100*103
=[(1-1/4)+(1/4-1/7)+……+(1/100-1/103)]/3
=(1-1/103)/3
=34/103