问题标题:
一道数学计算题……(7²+1/7²-1)+(9²+1/9²-1)+(11²+1/11²-1)……(99²+1/99²-1)把方法写下来~
问题描述:

一道数学计算题……

(7²+1/7²-1)+(9²+1/9²-1)+(11²+1/11²-1)……(99²+1/99²-1)

把方法写下来~

刘正喜回答:
  (7^2+1)/7^2-1+(9^2+1)/9^2-1+(11^2+1)/11^2-1+……+(99^2+1)/99^2-1   =[1+2/(7^2-1)]+[1+2/(9^2-1)]+[1+2/(11^2-1)]+……+[1+2/(99^2-1)]   =[1+2/(7-1)(7+1)]+[1+2/(9-1)(9+1)]+[1+2/(11-1)(11+1)]+……+[1+2/(99-1)(99+1)]   =47*1+2/(7-1)(7+1)+2/(9-1)(9+1)+2/(11-1)(11+1)+……+2/(99-1)(99+1)   =47+(1/6*8+1/8*10+1/10*12+……+1/98*100)*2   =47+(1/6-1/8+1/8-1/10+……+1/98-1/100)   =47+1/6-1/100   =47+94/600   =47+47/300
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