数学题在线解答1/(2*7)+1/(12*7)+1/(12*17)+1/(22*17)+.+1/(97*102)

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数学题在线解答1/(2*7)+1/(12*7)+1/(12*17)+1/(22*17)+.+1/(97*102)数学题在线解答1/(2*7)+1/(12*7)+1/(12*17)+1/(22*17)+

数学题在线解答1/(2*7)+1/(12*7)+1/(12*17)+1/(22*17)+.+1/(97*102)
数学题在线解答1/(2*7)+1/(12*7)+1/(12*17)+1/(22*17)+.+1/(97*102)

数学题在线解答1/(2*7)+1/(12*7)+1/(12*17)+1/(22*17)+.+1/(97*102)
原式=1/5×(1/2-1/7+1/7-1/12+1/12-1/17+.+1/97-1/102)
  =1/5×(1/2-1/102)
  =1/5×50/102
  =5/51

((1/2-1/7)+(1/7-1/12)+.....+(1/97-1/102))/5=(1/2-1/102)/5=5/51

由 1/(a*b)=1/(b-a)*[1/a-1/b]可得
所求等于1/5〔1/2-1/7+1/7-1/12+…+1/92-1/97+1/97-1/102〕=(1/5)*(1/2-1/102)=5/51