1/1×4+1/4×7+1/7×10+.+1/52×55+1/55×58

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1/1×4+1/4×7+1/7×10+.+1/52×55+1/55×58
1/1×4+1/4×7+1/7×10+.+1/52×55+1/55×58

1/1×4+1/4×7+1/7×10+.+1/52×55+1/55×58
裂项:原式=(1-1/4+1/4-1/7+1/7-1/10+……+1/52-1/55+1/55-1/58)/3=(1-1/58)/3=19/58

= (1/3)(1-1/58)
=19/58

原式=1/3 *(1-1/4)+1/3*(1/4-1/7)+1/3*(1/7-1/10)+........+1/3*(1/52-1/55)+1/3*(1/55-1/58) =1/3*(1-1/3+1/3-1/7+1/7-1/10+........+1/52-1/55+1/55-1/58)=1/3*(1-1/58)=1/3 *(57/58)=19/58