1+(1/1+2)+(1/1+2+3)+...+(1/1+2+3+...100)=?

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/05/03 01:54:51

1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...100)
=1+1/3+1/6+1/10+...+1/5050
=2/2+2/6+2/12+2/20+...+2/10100
=2/(1×2)+2/(2×3)+2/(3×4)+2/(4×5)+...+2/(100×101)
=2(1/1-1/2)+2(1/2-1/3)+2(1/3-1/4)+2(1/4-1/5)+...+2(1/100-1/101)
=2(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/100-1/101)
=2(1-1/101)
=200/101

(1/100-1)(1/99-1)(1/98-1)(1/97-1).(1/3-1)(1/2-1)= 200×(1-1/2)×(1-1/3)×(1-1/4)×……×(1-1/100)=? (1/100-1)(1/99-1).(1/3-1)(1/2-1)=? 1;(1-1/2^2)(1-1/3^2)(1-1/4^2)````````````(1-1/99^2)(1-1/100^ 1*2/1+2*3/1+3*4/1+.98*99/1+99*100/1=? (1-1/2)(1-1/3)(1-1/4).(1-1/99)(1-1/100)等于? 1+1+(1\1+2)+(1\1+2+3)+.(1\1+2+3.+100)等于多少 (-1*1\2)+(-1\2*1\3)+(-1\3*1\4)+.+(-1\99*1\100) 1+ 1/1+2 +1/1+2+3 +...+1/1+2+3+...100 1+(1+2)/1+(1+2+3)/1+...+(1+2+3+...+100)/1等于多少? 1+1+2/1+1+2+3/1+...+1+2+3+...+100/1怎么简算? 1 1 1 1------ + ------ + ------ + .+ -------------- =1×2 2×3