利用因式分解计算:(1-1/2²)(1-1/3²•……•(1-1/100²) 急用!
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利用因式分解计算:(1-1/2²)(1-1/3²•……•(1-1/100²) 急用!
利用因式分解计算:(1-1/2²)(1-1/3²•……•(1-1/100²) 急用!
利用因式分解计算:(1-1/2²)(1-1/3²•……•(1-1/100²) 急用!
平方差
=(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 前后抵消
=1/2×101/100
=101/200
=0.505
平方差
=(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 前后抵消
=1/2×101/100
=101/200
=0.505
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平方差
=(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 前后抵消
=1/2×101/100
=101/200
=0.505
不懂可追问 有帮助请采纳 祝你学习进步 谢谢
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(1-1/2²)(1-1/3²•……•(1-1/100²)
=(1+1/2)(1-1/2)(1+1/3)(1-1/3).....(1+1/100)(1-1/100)
=3/2*1/2*4/3*2/3*......*101/100*99/100
=1/2*101/100
=101/200
(1-1/2²)(1-1/3²)•……•(1-1/100²)
=[(2²-1)/2²][(3²-1)/3²]……[(100²-1)/100²]
=[(2-1)(2+1)/2²][(3-1)(3+1)/3²]……[(100-1)(100+1)/100²]
=(1*3/2²)(2*4/3²)……(99*101/100²)
=1/2*101/100
=101/200