1-1/2²=1-1/4=3/4=1/2x3/2 你能得出什么结论 (1-1/2²)x(1-1/3²)x····x(1-1/100)
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![1-1/2²=1-1/4=3/4=1/2x3/2 你能得出什么结论 (1-1/2²)x(1-1/3²)x····x(1-1/100)](/uploads/image/z/2102538-66-8.jpg?t=1-1%2F2%26%23178%3B%3D1-1%2F4%3D3%2F4%3D1%2F2x3%2F2+%E4%BD%A0%E8%83%BD%E5%BE%97%E5%87%BA%E4%BB%80%E4%B9%88%E7%BB%93%E8%AE%BA+%EF%BC%881-1%2F2%26%23178%3B%EF%BC%89x%EF%BC%881-1%2F3%26%23178%3B%EF%BC%89x%C2%B7%C2%B7%C2%B7%C2%B7x%EF%BC%881-1%2F100%EF%BC%89)
1-1/2²=1-1/4=3/4=1/2x3/2 你能得出什么结论 (1-1/2²)x(1-1/3²)x····x(1-1/100)
1-1/2²=1-1/4=3/4=1/2x3/2 你能得出什么结论 (1-1/2²)x(1-1/3²)x····x(1-1/100)
1-1/2²=1-1/4=3/4=1/2x3/2 你能得出什么结论 (1-1/2²)x(1-1/3²)x····x(1-1/100)
(1-1/2²)x(1-1/3²)x····x(1-1/100)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3).(1-1/100)(1+1/100)
=1/2x3/2x2/3x4/3x3/4x.x99/100x101/100
=1/2x1x1x...x1x101/100
=101/200
答案为:101/200
1-n的平方分之一=n分之一乘与n分之n的平方减一
1-1/3*1/3=1-1/9=8/9=1/3*(3*3-1)/3
(1-1/2²)x(1-1/3²)x····x(1-1/100)=200分之101
关键是找规律
得出的结论是1-1/n²=1/n×(n²-1)/n
(1-1/2²) x (1-1/3²)x......x (1-1/100)
=1/2 x 3/2x 1/3 x 8/3 x......1/10 x 99/10
=11/20