观察下面计算,情形1:2×2/1=4,2+2/1=4.情形2:3×3/2=9/2,3+3/2=9/2.情形3:4×4/3=16/3,4+4/3=16/3观察下面计算,情形1:2×2/1=4,2+2/1=4.情形2:3×3/2=9/2,3+3/2=9/2.情形3:4×4/3=16/3,4+4/3=16/3 (1)根据上述规律,写
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![观察下面计算,情形1:2×2/1=4,2+2/1=4.情形2:3×3/2=9/2,3+3/2=9/2.情形3:4×4/3=16/3,4+4/3=16/3观察下面计算,情形1:2×2/1=4,2+2/1=4.情形2:3×3/2=9/2,3+3/2=9/2.情形3:4×4/3=16/3,4+4/3=16/3 (1)根据上述规律,写](/uploads/image/z/14592942-54-2.jpg?t=%E8%A7%82%E5%AF%9F%E4%B8%8B%E9%9D%A2%E8%AE%A1%E7%AE%97%2C%E6%83%85%E5%BD%A21%EF%BC%9A2%C3%972%2F1%3D4%2C2%2B2%2F1%3D4.%E6%83%85%E5%BD%A22%EF%BC%9A3%C3%973%2F2%3D9%2F2%2C3%2B3%2F2%3D9%2F2.%E6%83%85%E5%BD%A23%EF%BC%9A4%C3%974%2F3%3D16%2F3%2C4%2B4%2F3%3D16%2F3%E8%A7%82%E5%AF%9F%E4%B8%8B%E9%9D%A2%E8%AE%A1%E7%AE%97%2C%E6%83%85%E5%BD%A21%EF%BC%9A2%C3%972%2F1%3D4%2C2%2B2%2F1%3D4.%E6%83%85%E5%BD%A22%EF%BC%9A3%C3%973%2F2%3D9%2F2%2C3%2B3%2F2%3D9%2F2.%E6%83%85%E5%BD%A23%EF%BC%9A4%C3%974%2F3%3D16%2F3%2C4%2B4%2F3%3D16%2F3+%EF%BC%881%EF%BC%89%E6%A0%B9%E6%8D%AE%E4%B8%8A%E8%BF%B0%E8%A7%84%E5%BE%8B%2C%E5%86%99)
观察下面计算,情形1:2×2/1=4,2+2/1=4.情形2:3×3/2=9/2,3+3/2=9/2.情形3:4×4/3=16/3,4+4/3=16/3观察下面计算,情形1:2×2/1=4,2+2/1=4.情形2:3×3/2=9/2,3+3/2=9/2.情形3:4×4/3=16/3,4+4/3=16/3 (1)根据上述规律,写
观察下面计算,情形1:2×2/1=4,2+2/1=4.情形2:3×3/2=9/2,3+3/2=9/2.情形3:4×4/3=16/3,4+4/3=16/3
观察下面计算,情形1:2×2/1=4,2+2/1=4.情形2:3×3/2=9/2,3+3/2=9/2.
情形3:4×4/3=16/3,4+4/3=16/3
(1)根据上述规律,写出情形n.
(2)根据共同特征,写出你的猜想,并证明你的猜想的正确性.
观察下面计算,情形1:2×2/1=4,2+2/1=4.情形2:3×3/2=9/2,3+3/2=9/2.情形3:4×4/3=16/3,4+4/3=16/3观察下面计算,情形1:2×2/1=4,2+2/1=4.情形2:3×3/2=9/2,3+3/2=9/2.情形3:4×4/3=16/3,4+4/3=16/3 (1)根据上述规律,写
n*n/(n-1)=n的平方/(n-1)----------------------公式A
n+n/(n-1)=n的平方/(n-1)---------------------公式B
公式A稍加运算就可以出来了
公式B左变=n*(n-1)/(n-1)+n/(n-1)
=(n*n-n+n)/(n-1)
=(n*n)/(n-1)
n*n/(n-1)=n*n/(n-1),n+n/(n-1)=n*n/(n-1)
证明:几所上面两式即可
n+1)×(n+1)/n=(n+1)×(n+1)/n,
(n+1)+(n+1)/n=(n+1)×(n+1)/n
(1)情形n:(n+1)×(n+1)/n=(n+1)×(n+1)/n,
(n+1)+(n+1)/n=(n+1)×(n+1)/n