简便计算1/6+1/12+1/20+1/30+.+1/2005*2006=
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![简便计算1/6+1/12+1/20+1/30+.+1/2005*2006=](/uploads/image/z/143880-24-0.jpg?t=%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%971%2F6%2B1%2F12%2B1%2F20%2B1%2F30%2B.%2B1%2F2005%2A2006%3D)
简便计算1/6+1/12+1/20+1/30+.+1/2005*2006=
简便计算1/6+1/12+1/20+1/30+.+1/2005*2006=
简便计算1/6+1/12+1/20+1/30+.+1/2005*2006=
1/6+1/12+1/20+1/30+.+1/2005*2006=
=[1/(2*3)]+[1/(3*4)]+[1/(4*5)]+[1/(5*6)]+……+[1/(2005*2006)]
=(1/2)-(1/3)+(1/3)-(1/4)+(1/4)-(1/5)+(1/5)-(1/6)+……+(1/2005)-(1/2006)
=(1/2)-(1/2006)
=1002/2006
=501/1003
1/6+1/12+1/20+1/30+.......+1/2005*2006=
(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+......+(1/2005-1/2006)
=1/2-1/2006=1002/2006=501/1003
原式= 1/(2*3) + 1/(3*4) +...+1/(2005*2006)
= 1/2 - 1/3 + 1/3 - 1/4 + ... +1/2005 - 1/2006
= 1/2 - 1/2006
= 501/1003
501/1003