如题所述
1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)-~~~~~~~~~1/(199*200)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5~~~~~~~~+1/199-1/200
=1-1/200
=199/200
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5~~~~~~~~+1/199-1/200
=1-1/200
=199/200
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第1个回答 2011-07-01
1/n(n+1)=1/n-1/(n+1)
因此
一乘二分之一加二乘三分之一加.............加一百九十九乘二百分之一
=1-1/2+1/2-1/3+1/3-1/4+……+1/199-1/200
=1-1/200
=199/200
因此
一乘二分之一加二乘三分之一加.............加一百九十九乘二百分之一
=1-1/2+1/2-1/3+1/3-1/4+……+1/199-1/200
=1-1/200
=199/200
