观察下列算式:1-1/2次方=3/4=1/2*3/2,(1-1/2次方)(1-1/3次方)=3/4*8/9=1/2*3/2*2/3*4/3,.(1)、研究上面算式,你发现什么规律?请用你的发现计算:(1-1/2次方)(1-1/3次方)(1-1/4次方).(1-1/100次方)=(2
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![观察下列算式:1-1/2次方=3/4=1/2*3/2,(1-1/2次方)(1-1/3次方)=3/4*8/9=1/2*3/2*2/3*4/3,.(1)、研究上面算式,你发现什么规律?请用你的发现计算:(1-1/2次方)(1-1/3次方)(1-1/4次方).(1-1/100次方)=(2](/uploads/image/z/144875-11-5.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E7%AE%97%E5%BC%8F%3A1-1%2F2%E6%AC%A1%E6%96%B9%3D3%2F4%3D1%2F2%2A3%2F2%2C%281-1%2F2%E6%AC%A1%E6%96%B9%29%281-1%2F3%E6%AC%A1%E6%96%B9%EF%BC%89%3D3%2F4%2A8%2F9%3D1%2F2%2A3%2F2%2A2%2F3%2A4%2F3%2C.%EF%BC%881%EF%BC%89%E3%80%81%E7%A0%94%E7%A9%B6%E4%B8%8A%E9%9D%A2%E7%AE%97%E5%BC%8F%2C%E4%BD%A0%E5%8F%91%E7%8E%B0%E4%BB%80%E4%B9%88%E8%A7%84%E5%BE%8B%3F%E8%AF%B7%E7%94%A8%E4%BD%A0%E7%9A%84%E5%8F%91%E7%8E%B0%E8%AE%A1%E7%AE%97%EF%BC%9A%EF%BC%881-1%2F2%E6%AC%A1%E6%96%B9%EF%BC%89%EF%BC%881-1%2F3%E6%AC%A1%E6%96%B9%EF%BC%89%EF%BC%881-1%2F4%E6%AC%A1%E6%96%B9%EF%BC%89.%281-1%2F100%E6%AC%A1%E6%96%B9%EF%BC%89%3D%EF%BC%882)
观察下列算式:1-1/2次方=3/4=1/2*3/2,(1-1/2次方)(1-1/3次方)=3/4*8/9=1/2*3/2*2/3*4/3,.(1)、研究上面算式,你发现什么规律?请用你的发现计算:(1-1/2次方)(1-1/3次方)(1-1/4次方).(1-1/100次方)=(2
观察下列算式:1-1/2次方=3/4=1/2*3/2,(1-1/2次方)(1-1/3次方)=3/4*8/9=1/2*3/2*2/3*4/3,.
(1)、研究上面算式,你发现什么规律?请用你的发现计算:(1-1/2次方)(1-1/3次方)(1-1/4次方).(1-1/100次方)=
(2)、计算:(1-1/2次方)(1-1/3次方)(1-1/4次方).(1-1/n次方)=
观察下列算式:1-1/2次方=3/4=1/2*3/2,(1-1/2次方)(1-1/3次方)=3/4*8/9=1/2*3/2*2/3*4/3,.(1)、研究上面算式,你发现什么规律?请用你的发现计算:(1-1/2次方)(1-1/3次方)(1-1/4次方).(1-1/100次方)=(2
(1)、研究上面算式,你发现什么规律?请用你的发现计算:
(1-1/2次方)(1-1/3次方)(1-1/4次方).(1-1/100次方)
=(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×(1+1/4)×(1-1/4)×……×(1+1/100)×(1-1/100)
=3/2×4/3×5/4×……×101/100×1/2×2/3×3/4×……×1/100
=101/2×1/100
=101/200
(2)、计算:(1-1/2次方)(1-1/3次方)(1-1/4次方).(1-1/n次方)
=(1+1/2)×(1-1/2)×(1+1/3)×(1-1/3)×(1+1/4)×(1-1/4)×……×(1+1/n)×(1-1/n)
=3/2×4/3×5/4×……×(n+1)/n×1/2×2/3×3/4×……×1/n
=(n+1)/2×1/n
=(n+1)/2n
原式=1x1/2x2x1/3x3x1/4x4x1/5x.........x99x1/100
=(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*(1+1/4)*(1-1/4)*……*(1+1/n)*(1-1/n)
=3/2*4/3*……*(n+1)/n*1/2*2*3*……*(n-1)/n
=(n+1)/2*1/n
=(n+1)/2n