1/1*2*3+1/2*3*4+...+1/2008*1/2009*1/2010=
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1/1*2*3+1/2*3*4+...+1/2008*1/2009*1/2010=
1/1*2*3+1/2*3*4+...+1/2008*1/2009*1/2010=
1/1*2*3+1/2*3*4+...+1/2008*1/2009*1/2010=
首先,1/(n(n+1)(n+2))=1/2[1/(n(n+1))-1/((n+1)(n+2))]
所以,1/1*2*3=1/2[1/1*2-1/2*3]
1/2*3*4=1/2[1/2*3-1/3*4]
.
1/2008*1/2009*1/2010=1/2[1/2008*2009-1/2009*2010]
1/1*2*3+1/2*3*4+...+1/2008*1/2009*1/2010=1/2[1/1*2-1/2009*2010]=504761/2019045