1 / 2 × 2 / 3 × 3 / 4 ×... × 99 / 100. What is the product of 99 fractions?

1 / 2 × 2 / 3 × 3 / 4 ×... × 99 / 100. What is the product of 99 fractions?

1/2×2/3×3/4×...×99/100
=1/100

According to the law of the following numbers, the 99th number is {} and the 2012 number is {} minus one-half
According to the law of the following numbers, the 99th number is {} and the 2012 number is {}
One half, one third, one fourth, one fifth and one sixth

-99
1/2012

(1 + 1 / 2) times (1-2 / 3) times (1 + 2 / 3) times (1-1 / 4)

(1 + 1 / 2) times (1-2 / 3) times (1 + 2 / 3) times (1-1 / 4)
The results are as follows
(1+1/2)*(1-1/4)*[(1-2/3)*(1+2/3)]
==(1+1/2)*(1-1/4)*(1-4/9)
==(3/2)*(3/4)(5/9)
==(9/8)*(5/9)
==5/8