1/1*5+1/5*10+1/10*15+···· - 知识问答

1/1*5+1/5*10+1/10*15+······+1/45*50=

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1/1*5+1/5*10+1/10*15+······+1/45*50
=1/5+1/5[(1/5-1/10)+(1/10-1/15)+……+(1/45-1/50)]
=1/5+1/5×(1/5-1/10+1/10-1/15+……+1/45-1/50)
=1/5+1/5×(1/5-1/50)
=1/5+1/5×9/50
=50/250+9/250
=59/250

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