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(1-4/1)(1-9/1)(1-16/1).......(1-81/1)(1-1...

解:(1-1/4)(1-1/9).....(1-1/100)=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/9)(1+1/9)(1-1/10)(1+1/10)=1/2*3/2*2/3*4/3*3/4*...8/9*10/9*9/10*11/10观察有很多项约掉了,最后得:=1/2*11/10=11/20满意谢谢采纳!

(n+1)/2n

.................

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).......(1-1/10000) =(1-1/2^2)(1-1/3^2)......(1-1/20^2) =(1-1/2)(1+1/2)(1-1/3)(1+1/3).....(1-1/20)(1+1/20) =1/2*3/2*2/3*4/3.....19/20*21/20 =21/2

1-1/n^2=(n-1)(n+1)/n^2 (1-1/4)(1-1/9)(1-1/16)......(1-1/81)(1-1/100)......(1-1/n的平方) =(1-1/2^2)(1-1/3^2)(1-1/4^2)(1-1/5^2)...(1-1/n^2) =1*3/2^2*2*4/3^2*3*5/4^2*4*6/5^2*...(n-1)(n+1)/n^2 =1*(n+1)/(2*n) =(n+1)/(2n)

(1-1/4)(1-1/9)(1-1/16)...(1-1/100) =(1-1/2²)(1-1/3²)(1-1/4²)...(1-1/10²) =(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4)...(1+1/10)(1-1/10) =(3/2)(1/2)(4/3)(2/3)(5/4)(3/4)...(11/10)(9/10) =[(1/2)(2/3)...(9/10)][...

解:原式=(-1/2)×(-2/3)×(-3/4)×(-4/5)×……×(-99/100) 共有99个负数相乘 =-(1/2×2/3×3/4×4/5×……×99/100) 从第一个分数开始,前面的分数的分母可以与后面分数的分子约分,最后剩下第一个分数的分子1和最后一个分数分母100没有约分 = -1/100

(1/2+1/4+1/6+1/8)-(1/3+1/6+1/9+1/12)+(1/4+1/8+1/12+1/16)-(1/5+1/10+1/15+1/20) =1/2(1+1/2+1/3+1/4)-1/3(1+1/2+1/3+1/4)+1/4(1+1/2+1/3+1/4)-1/5(1+1/2+1/3+1/4) =(1+1/2+1/3+1/4)(1/2-1/3+1/4-1/5) =(12+6+4+3)/12*(30-20+15-12)/6...

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

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