1/6+1/12+1/20+1/30+···+1/2005X2006=?分数简便运算

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1/6+1/12+1/20+1/30+···+1/2005X2006=?分数简便运算1/6+1/12+1/20+1/30+···+1/2005X2006=?分数简便运算1/6+1/12+1/20+1/

1/6+1/12+1/20+1/30+···+1/2005X2006=?分数简便运算
1/6+1/12+1/20+1/30+···+1/2005X2006=?
分数简便运算

1/6+1/12+1/20+1/30+···+1/2005X2006=?分数简便运算
1/6+1/12+1/20+1/30+···+1/2005X2006
=1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+...+1/(2005X2006)
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+...+(1/2005-1/2006)
=1/2-1/2006
=501/1003