1乘2乘3分之1+2乘3乘4分之1+...+98乘99乘100分之1 这题怎么写,用简便算法
1乘2乘3分之1+2乘3乘4分之1+...+98乘99乘100分之1 这题怎么写,用简便算法
数学人气:131 ℃时间:2019-09-26 00:53:09
优质解答
1/1*2*3+1/2*3*4+1/3*4*5+……+1/98*99*100=1/2(2/1*2*3+2/2*3*4+……2/98*99*100)=1/2(1/1*2-1/2*3+1/2*3-1/3*4+……+1/98*99-1/99*100)=1/2(1/1*2-1/99*100)=1/2*4949/9900=4949/19800
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