Question

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

Answer 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

Answer 2

n﹡n/(n+1)=n-n/(n+1)

Answer 3

1.n*n/n+1=n-n/n+1