如题所述
第1个回答 2015-11-29
用平方差公式分解每一个因式,
(1-1/4)(1-1/9)(1-1/16).......(1-1/10000)
=(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,
注意中间每两个分数的积为1,所以
原式=1/2×101/100=101/200.
(1-1/4)(1-1/9)(1-1/16).......(1-1/10000)
=(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,
注意中间每两个分数的积为1,所以
原式=1/2×101/100=101/200.
第2个回答 2014-10-26
(1-1/4)(1-1/9)(1-1/16).......(1-1/10000)
=(1-1/2^2)(1-1/3^2)......(1-1/100^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3).....(1-1/100)(1+1/100)
=1/2*3/2*2/3*4/3.....99/100*101/100
=101/2本回答被提问者采纳
=(1-1/2^2)(1-1/3^2)......(1-1/100^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3).....(1-1/100)(1+1/100)
=1/2*3/2*2/3*4/3.....99/100*101/100
=101/2本回答被提问者采纳