Interesting

Alternatively, wrote this into $\displaystyle 1-\frac{2}{n+1}$ . This form will produce a fraction which does not become 1 as $n\to\infty$ . While it forms a sequence, the most correct answer is $\lim_{n\to\infty}\frac{n-1}{n+1} =\lim_{n\to\infty} 1-\frac{2}{n+1}=1$ Which means it get closes to 1 when $n$ is larger, but the exact value is not 1.

If n is 3, the number would be $\frac{2}{4}$ , which equals to half. But let's say n is a very large number, like 10 trillion. The number would be $\frac{10 trillion-1}{10 trillion+1}$ . If we turn this in to a decimal number, it turns out that it's sooooooo close to 1 that even calculator says it's one. Also using the fact that 0.999...999 is 1, we are sure that the number should be 1. But remember, it's approximately 1. So it's not 1, but close enough to be 1.

The answer is 1 Use the force then, you will truly understand......... Join the Dark Side!!! -Darth Vegy-
AOJ-CEO May the Force be with you