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解一下这道题1/5X9+1/9X13+1/13X17+...1/101X105=?
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解一下这道题1/5X9+1/9X13+1/13X17+...1/101X105=?
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答案和解析
1/5X9+1/9X13+1/13X17+...1/101X105
=(1/4)*(1/5-1/9)+(1/4)*(1/9-1/13)+(1/4)*(1/13-1/17)+.+(1/4)*(1/101-1/105)
=(1/4)*(1/5-1/9+1/9-1/13+1/13-1/17+.+1/101-1/105)
=(1/4)*(1/5-1/105)
=(1/4)*(4/21)
=1/21
=(1/4)*(1/5-1/9)+(1/4)*(1/9-1/13)+(1/4)*(1/13-1/17)+.+(1/4)*(1/101-1/105)
=(1/4)*(1/5-1/9+1/9-1/13+1/13-1/17+.+1/101-1/105)
=(1/4)*(1/5-1/105)
=(1/4)*(4/21)
=1/21
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