觀察下麵的變形規律: 1/(1*2)=1-1/2;1/(2*3)=1/2-1/3;1/(3*4)=1/3-1/4;…….求和:1/(1*2)+1/(2*3)+1/(3*4)+…..+1/(2009*2010)

觀察下麵的變形規律: 1/(1*2)=1-1/2;1/(2*3)=1/2-1/3;1/(3*4)=1/3-1/4;…….求和:1/(1*2)+1/(2*3)+1/(3*4)+…..+1/(2009*2010)

1/(1*2)=1-1/2;1/(2*3)=1/2-1/3;1/(3*4)=1/3-1/4;…….
所以1/(1*2)+1/(2*3)+1/(3*4)+…..+1/(2009*2010)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1-1/2010
=2009/2010