观察下列等式:1x1/2=1-1/2,2x2/3=2-2/3,3x3/4=3-3/4,……1.猜想并写出第n个等式.2.请你计算:(1-1/2)/10x(2-2/3)/9x(3-3/4)/8x.x(10-10/11)/1
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![观察下列等式:1x1/2=1-1/2,2x2/3=2-2/3,3x3/4=3-3/4,……1.猜想并写出第n个等式.2.请你计算:(1-1/2)/10x(2-2/3)/9x(3-3/4)/8x.x(10-10/11)/1](/uploads/image/z/10390107-3-7.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E7%AD%89%E5%BC%8F%EF%BC%9A1x1%2F2%3D1-1%2F2%2C2x2%2F3%3D2-2%2F3%2C3x3%2F4%3D3-3%2F4%2C%E2%80%A6%E2%80%A61.%E7%8C%9C%E6%83%B3%E5%B9%B6%E5%86%99%E5%87%BA%E7%AC%ACn%E4%B8%AA%E7%AD%89%E5%BC%8F.2.%E8%AF%B7%E4%BD%A0%E8%AE%A1%E7%AE%97%3A%281-1%2F2%29%2F10x%282-2%2F3%29%2F9x%283-3%2F4%29%2F8x.x%2810-10%2F11%29%2F1)
观察下列等式:1x1/2=1-1/2,2x2/3=2-2/3,3x3/4=3-3/4,……1.猜想并写出第n个等式.2.请你计算:(1-1/2)/10x(2-2/3)/9x(3-3/4)/8x.x(10-10/11)/1
观察下列等式:1x1/2=1-1/2,2x2/3=2-2/3,3x3/4=3-3/4,……
1.猜想并写出第n个等式.
2.请你计算:(1-1/2)/10x(2-2/3)/9x(3-3/4)/8x.x(10-10/11)/1
观察下列等式:1x1/2=1-1/2,2x2/3=2-2/3,3x3/4=3-3/4,……1.猜想并写出第n个等式.2.请你计算:(1-1/2)/10x(2-2/3)/9x(3-3/4)/8x.x(10-10/11)/1
解1:
第n个等式是:n×(n/(n+1)=n-n/(n+1)
解2:
[(1-1/2)/10]×[(2-2/3)/9]×[(3-3/4)/8]×……×[(10-10/11)/1]
=[(1×1/2)/10]×[(2×2/3)/9]×[(3×3/4)/8]×……×[(10×10/11)/1]
=[(1×1/2)/1][(2×2/3)/2][(3×3/4)/3]×……×[(10×10/11)/10]
=(1/2)[(2×2/3)/2][(3×3/4)/3]×……×[(10×10/11)/10]
=(1/3)[(3×3/4)/3]×……×[(10×10/11)/10]
=(1/4)[(4×4/5)/4]×……×[(10×10/11)/10]
=(1/5)[(5×5/6)/5]×……×[(10×10/11)/10]
=(1/6)[(6×6/7)/6]×……×[(10×10/11)/10]
=(1/7)[(7×7/8)/7]×……×[(10×10/11)/10]
=(1/8)[(8×8/9)/8]×……×[(10×10/11)/10]
=(1/9)[(9×9/10)/9]×[(10×10/11)/10]
=(1/10)[(10×10/11)/10]
=1/11
1.n*n/n+1=n-n/n+1
n﹡n/(n+1)=n-n/(n+1)