问题标题:
【简便计算1/6+1/12+1/20+1/30+.+1/2005*2006=】
问题描述:
简便计算1/6+1/12+1/20+1/30+.+1/2005*2006=
何银南回答:
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
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