1 1 1 1------ + ------ + ------ + .+ -------------- =1×2 2×3
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/15 18:21:51
1 1 1 1
------ + ------ + ------ + .+ -------------- =
1×2 2×3 3×4 2009×2010
1 1 1 1
---------- + --------- + ---------- + .+ -----------=
10×16 16×22 22×28 94×100
------ + ------ + ------ + .+ -------------- =
1×2 2×3 3×4 2009×2010
1 1 1 1
---------- + --------- + ---------- + .+ -----------=
10×16 16×22 22×28 94×100
1 1 1 1
------ + ------ + ------ + .+ --------------
1×2 2×3 3×4 2009×2010
=1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1-1/2010=2009/2010
2.
------ + ------ + ------ + .+ --------------
1×2 2×3 3×4 2009×2010
=1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1-1/2010=2009/2010
2.
1 1 1 1------ + ------ + ------ + .+ -------------- =1×2 2×3
(1\2012-1)(1\2011-1)(1\2010-1)...(1\3-1)(1\2-1)=?
(1/1+2)+(1/1+2+3)+...+(1/1+2+3+4+...+50) = (1+1/51)*(1-1/51)
1+1/1+2+1/1+2+3...+1/1+2+3+...+n=
1/1×2+1/1-1/2:;1/2×4=1/2×(1/2-1/4);1/58×=1/3(×1/5-1/8)
(1/100-1)(1/99-1)(1/98-1)(1/97-1).(1/3-1)(1/2-1)=
1+1=?1+2=?1+3=?
观察下列各式:1/1*2=1/1-1/2,1/2*3=1/2-1/3,1/3*4=1/3-1/4.
设S1=1+1/(1^2)+1/(2^2),S2=1+1/(2^2)+1/(3^2),S3=1+1/(3^2)+1/(4
(1-1/2)×(1-3/1)×.×(1-1/2008)×(1-1/2009)=?
2007*(1-1/2)*(1-1/3)*(1-1/4).(1-1/2007)=?
200×(1-1/2)×(1-1/3)×(1-1/4)×……×(1-1/100)=?