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(1-1/4)(1-1/9)(1-1/16)···(1-1/100)

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

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

(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

1+2*2+3*3+...+n*n=1+1*2+2+2*3+3+3*4+4+....(n-1)n+n =(1+2+3+...+n)+[1*2+2*3+3*4+....(n-1)*n] =n(n+1)/2+[1*2*3+2*3*3+3*4*3+....(n-1)*n*3]/3 =n(n+1)/2+[1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+......(n-1)n(n+1)-(n-2)(n-1)n]/3 =n(n+1)/2+(n-1)...

1-1/n^2=(n-1)(n+1)/n² 原式=(1/2) *(3/2) * (2/3) *(4/3) * (3/4)*(5/4) *.......*98/99 * 100/99 =(1/2) * (100/99) =50/99

题目有问题,前后数没有规律,不能确定个数。

解: (1-1/4)*(1-1/9)*(1-1/16)*(1-1/25)...*(1-1/100) =(1+1/2)(1-1/2) *(1+1/3)(1-1/3) *... *(1+1/10)(1-1/10) =3/2 *1/2 *4/3 *2/3 *5/4 *3/4 *..... *11/10 *9/10 =(3/2 *4/3 *5/4 *...*11/10) * (1/2 *2/3 *3/4 *...*9/10) =11/2*1/10 =1...

新建一个窗体,在窗体中添加一个text1和一个command1,双击command1添加如下代码: s=0 for i=1 to 10 s=s+1/(i*i) next text1.text=s

1/(1+2+3+……+9)+1/(1+2+3+……+10)+1/(1+2+3+……+11)+1/(1+2+3+……+12)+....+1/(1+2+3+……+100) =2/(9×10)+2/(10×11)+2/(11×12)+2/(12×13)+....+2/(100×101) =2×(1/9-1/10+1/10-1/11+1/11-1/12+1/12-1/13+……+1/100-1/101) =2×(1/9-1/101) =2×92/9...

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