1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+........1/(20x21x22)=?

显示全部楼层 · 2007-3-26 17:52:31

1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+.........1/(20*21*22) =1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22] =1/2[1/2-1/21*22] =1/2*115/231 =115/462

千问 · 2007-3-26 17:52:31

1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+.........1/(20*21*22)=1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22]=1/2[1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+1/20*21-1/21*22]=1/2[1/2-1/21*22]=1/2*115/231=115/462祝你学习进步！天天快乐！加油！