(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2010^2)
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/31 16:38:19
(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2010^2)
原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/2010)(1+1/2010)
=1/2×3/2×2/3×4/3×3/4×5/4×...×2009/2010×2011/2010
=1/2×2011/2010
=2011/4020
=1/2×3/2×2/3×4/3×3/4×5/4×...×2009/2010×2011/2010
=1/2×2011/2010
=2011/4020
(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2010^2)
计算:(1+1/2)(1+1/3)(1+1/4)…(1+1/2010)(1/2-1)(1/3-1)(1/4-1)…(1/
1/1*2+1/2*3+1/3*4+……+1/2010*2011
1+1\(1+2)+1\(1+2+3)+1\(1+2+3+4)+……1\(1+2+3+……2010)
1/1×2+1/2×3+1/3×4+…+1/2010×2011+1/2012×2013
1/1×2+1/2×3+1/4×5+……+1/2009×2010
(2011/1-1)(2010/1-1)(2009/1-1)…(3/1-1)(2/1-1)
用简便算法计算:(1-1/2-1/3-1/4-…-1/2010)×(1/2+1/3+1/4+…+1/2010)-(1-1
1/(1-1/2)/(1-1/3)/(1-1/4)/……/(1-1/2012)
|1/3+(-1/2)|+|1/4+(-1/3)|+|1/5+(-1/4)|+……+|1/2010+(-1/2009)|
1*2/1+2*3/1+3*4/1+…2010*2011/1等于?
(1-2/1)(3/1-1)(1-4/1)(5/1-1)(1-6/1)……(1-2010/1)(2011/1-1)