Question

已知S=1X2X3+2X3X4+3X4X5+……+2007X2008X2009,求出4XS/(2007X2008X200

Answer 1

S=∑(n(n+1)(n+2)=)∑(n³+3n²+2n）=(n(n+1)/2)^2+3n(n+1)(2n+1))/6+2n×(n+1)/2;

4S=n(n+1)^2+2n(n+1)(2n+1)+4n(n+1)=n(n+1)(n²+5n+6)=n(n+1)(n+2)(n+3);

4S/(2007X2008X2009)=(2007×2008×2009×2010)/(2007×2008×2009)=2010.完