Question

1-1/2 * 1-1/3 * 1-1/4* 1-1/5........1-1/999
How do you solve this?

Answer 1

Answer: The answer would simply be 500

Answer 2

`1(1)/(2)\cdot 1(1)/(3)\cdot1(1)/(4)\cdot\ldots \cdot 1(1)/(999)=\\\\ (3)/(2)\cdot(4)/(3)\cdot(5)/(4)\cdot\ldots\cdot(1000)/(999)=\\\\ ((1000!)/(2))/(999!)=\\\\ (1000!)/(2\cdot999!)=\\\\ (1000)/(2)=\\\\ 500`