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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