(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/20²)用简便算法计算
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(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/20²)用简便算法计算
(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/20²)用简便算法计算
(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/20²)用简便算法计算
原式=(1+1/2)(1-1/2)(1+1/3)(1-1/3)...(1+1/20)(1-1/20)(运用平方差公式)
=3/2*1/2*4/3*2/3...*19/20*21/20(2/3*3/2=1,省略,后面以此类推)
=1/2*21/20
=21/40
(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/20²)
=(2²-1)(3²-1)....(20²-1)/(2²*3²....20²)
=(2+1)(2-1)(3+1)(3-1)....(20+1)(20-1)/(2²*3²....20²)...
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(1-1/2²)(1-1/3²)(1-1/4²)…(1-1/20²)
=(2²-1)(3²-1)....(20²-1)/(2²*3²....20²)
=(2+1)(2-1)(3+1)(3-1)....(20+1)(20-1)/(2²*3²....20²)
=(3*4*5*...21)(1*2*3*....19)/(2²*3²....20²)
=1*20*21/(2²*20²)
=21/80
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