大师作文网(1-1/2-1/3-...-1/2009)(1/2+1/3+1/4...+1/2010)-(1-1/2-1/3-...
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/11/13 00:39:37
(1-1/2-1/3-...-1/2009)(1/2+1/3+1/4...+1/2010)-(1-1/2-1/3-...-1/2009-1/2010)(1/2+1/3...+1/2009)
let
x =1/2+1/3+...+1/2009
(1-1/2-1/3-...-1/2009)(1/2+1/3+1/4...+1/2010)-(1-1/2-1/3-...-1/2009-1/2010)(1/2+1/3...+1/2009)
= (1-x)(x+1/2010)- (1-x-1/2010)x
= [x+1/2010 - x^2 - x/2010] - [ x- x^2 -x/2010]
= 1/2010
x =1/2+1/3+...+1/2009
(1-1/2-1/3-...-1/2009)(1/2+1/3+1/4...+1/2010)-(1-1/2-1/3-...-1/2009-1/2010)(1/2+1/3...+1/2009)
= (1-x)(x+1/2010)- (1-x-1/2010)x
= [x+1/2010 - x^2 - x/2010] - [ x- x^2 -x/2010]
= 1/2010
(1-1/2-1/3-...-1/2009)(1/2+1/3+1/4...+1/2010)-(1-1/2-1/3-...
-1+2-3+4...-99+100 1/1×2+1/2×3+1/3×4+...+1/2009×2010+1/2010×
(2011/1-1)(2010/1-1)(2009/1-1)…(3/1-1)(2/1-1)
(1/2010-1)*(1/2009-1)*(1/2008-1)*...*(1/3-1)*(1/2-1)
(1-1/2)(1/3-1)(1-1/4)(1/5-1)``````(1/2009)(11/2010)
|1/2011-1/2010|+|1/2011-1/2009|+|1/2009-1/2008|+...+|1/3-1/2
｜1/2-1｜+｜1/3-1/2｜+1/4-1/3｜+...｜1/2009-1/2008｜+｜1/2010-1/2009
(-1*1/2) (-1/2*1/3) (-1/3*1/4) .(-1/2009*1/2010) (-1/2010*1/
计算(1-1/2)^2*(1-1/3)^2*(1-1/4)^2*...*(1-1/2009)^2*(1-1/2010)^
(1/2010*1/2009*1/2008*...*1/3*1/2*1)^2011*(2010*2009*2008*..
(1/2011*1/2010*1/2009*...1/3*1/2*1)∧2011*(2011*2010*2009*...
计算1/1*2010+1/2*2009+1/3*2008+...+1/2010*1-2010/2011（1/1*2009