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(1-1/4)1-1/9括号1-1/16省略号括号1-1/百

根据平方差公式, 原式 = (1-1/2)(1+1/2) * (1-1/3)(1+1/3) * (1-1/4)(1+1/4) *......*(1-1/100)(1+1/100) = 1/2*3/2*2/3*4/3*3/4*5/4*......*99/100*101/100 = 1/2*101/100 = 101/200

(3/4-1/16)×(1/9+1/3)用递等式计算 =(12/16-1/16)x(1/9+3/9) =11/16x4/9 =11/36

1-1/4=(1-1/2)(1+1/2)=1/2*3/2 1-1/9=(1-1/3)(1+1/3)=2/3*4/3 ... 1-1/100=(1-1/10)(1+1/10)=9/10*11/10 (1-1/4)(1-1/9)(1-1/16)···(1-1/100) =(1/2*3/2)*(2/3*4/3)*...*(9/10*11/10) =(1/2*2/3*3/4*...*9/10)*(3/2*4/3*5/4*...*11/10) =1/10*1...

(n+1)/2n

(1-1/4)×(1-1/9)×(1-1/16)×...×(1-1/4052169) =[(2²-1)/2²][(3²-1)/3²][(4²-1)/4²]...[(2013²-1)/2013²] =[(2+1)(2-1)/2²][(3+1)(3-1)/3²][(4+1)(4-1)/4²]...[(2013+1)(2013-1)/2013...

2011-03-19 (1-1/4)*(1-1/9)*(1-1/16). . .(... 40 2013-11-04 (-81)÷2又4分之1+9分之4÷(-16) 1 2014-04-13 1,4,9,16,25...

(1-1/4) (1-1/9) (1-1/16).....(1-1/81) (1-1/100) =[1-1/2][1+1/2][1-1/3][1+1/3][1-1/4][1+1/4]...[1-1/9][1+1/9][1-1/10][1+1/10] =1/2*3/2*2/3*4/3*3/4*5/4*...*8/9*10/9*9/10*11/10 =1/2*11/10 =11/20

查常用级数表就知道括号内=π^2/6 所以答案是:1/6

1+1/4+1/9.+1/N^2 =1+1/2*2+1/3*3+...1/N*N <1+1/1*2+1/2*3.+1/(N-1)N =1+1-(1/2)+(1/2)-(1/3).-1/N =2-1/N 所以原式成立

原式 =(1-1/2)(1+1/2) * (1-1/3)(1+1/3) * ... * (1-1/10)(1+1/10) =1/2 * 2/3 * 3/4 * ... * 9/10 * 3/2 * 4/3 * 5/4 * ... * 11/10 整理,抵消 =1/2 * 11/10 =11/20

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