10/(1*2)+20/(1*2*3)+30/(1*2*3*4)+40/(1*2*3*4*5)+...+90/(1*2*3*4*5*6*4*8*9*10)=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/09 17:17:59
10/(1*2)+20/(1*2*3)+30/(1*2*3*4)+40/(1*2*3*4*5)+...+90/(1*2*3*4*5*6*4*8*9*10)=?

10/(1*2)+20/(1*2*3)+30/(1*2*3*4)+40/(1*2*3*4*5)+...+90/(1*2*3*4*5*6*4*8*9*10)=?
10/(1*2)+20/(1*2*3)+30/(1*2*3*4)+40/(1*2*3*4*5)+...+90/(1*2*3*4*5*6*4*8*9*10)=?

10/(1*2)+20/(1*2*3)+30/(1*2*3*4)+40/(1*2*3*4*5)+...+90/(1*2*3*4*5*6*4*8*9*10)=?
原式+10/(1*2*3*4*5*6*4*8*9*10)
=10/(1*2)+……+80/1*2*3*4*5*6*4*8*9)+90/(1*2*3*4*5*6*4*8*9*10)+10/(1*2*3*4 *5*6*4*8*9*10)
=10/(1*2)+……+80/1*2*3*4*5*6*4*8*9)+ 100/(1*2*3*4*5*6*4*8*9*10)
=10/(1*2)+……+80/1*2*3*4*5*6*4*8*9)+ 10/(1*2*3*4*5*6*4*8*9)
=…………
=10/(1*2)+10/(1*2)
=10
所以原式=10-10/(1*2*3*4*5*6*4*8*9*10)
=多少自己算

原式最后一项加上10/(1*2*3*4*5*6*7*8*9*10),约去分母的10再与前一项相加,以此类推,最后减去上面的这个数就是结果

因为不管1的几次方都等于1,所以原式=10+20+。。。+90=450