数学题1/2*5+1/5*8+1/8*11+...+1/2003*2006

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数学题1/2*5+1/5*8+1/8*11+...+1/2003*2006数学题1/2*5+1/5*8+1/8*11+...+1/2003*2006数学题1/2*5+1/5*8+1/8*11+...+

数学题1/2*5+1/5*8+1/8*11+...+1/2003*2006
数学题1/2*5+1/5*8+1/8*11+...+1/2003*2006

数学题1/2*5+1/5*8+1/8*11+...+1/2003*2006
1/2*5+1/5*8+1/8*11+...+1/2003*2006
=1/3【(1/2-1/5)+(1/5-1/8)+.+(1/2003-1/2006)】
=1/3*(1/2-1/2006)=1/3*1002/2006
=167/1003

1/2*5+1/5*8+1/8*11+...+1/2003*2006
=1/3(1/2-1/5+1/5-1/8+1/8-1/11+...+1/2003-1/2006)
=1/3(1/2-1/2006)
=1/2*501/1003
=501/2006

1/(2*5)=1/3(1/2-1/5)
1/(5*8)=1/3(1/5-1/8)
1/2*5+1/5*8+1/8*11+...+1/2003*2006
=1/3(1/2-1/5+1/5-1/8+........+1/2003 -1/2006)
=1/3*(1/2-1/2006)
=1002/3*2006
=167/1003

1/2*5+1/5*8+1/8*11+...+1/2003*2006
=(1/2-1/5+1/5-1/8+...+1/2003-1/2006)/3
=(1/2-1/2006)/3
=167/1003

原式=1/3(1/2-1/5+1/5-1/8+1/8-1/11+ +1/2003-1/2006)
=1/3(1/2-1/2006)
=167/1003

原式=(1/3)*(1/2-1/5+1/5-1/8+1/8-1/11+....+1/2003-1/2006)
=(1/3)*(1/2-1/2006)
=167/1003

从题目看到其实它其实就是1/(n*(n+3),可以把它拆成1/3*(1/n-1/(n+3)),那么等式=1/3*(1/2-1/2006)=167/1003