观察下列等式:1x1/2=1-1/2,2x2/3=2-2/3,3x3/4=3-3/4,……

3个回答

  • 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