Help proving Sequences

[ChocoBard]

I need some help proving something with a sequence. Given M, a positive number that is less than 1, I need to prove that {n/(n+1)}_n=1^inf exceeds M for a sufficiently large n. Or in simpler terms, prove that n/(n+1) > M whenever n > N for some integer N.

I know that since the sequence goes to infinity, it can be seen as lim n→inf (n/(n+1)) is one, so I know that it's true, but how do I show that it's true?

 

[Deleted member 4993]

I need some help proving something with a sequence. Given M, a positive number that is less than 1, I need to prove that {n/(n+1)}_n=1^inf exceeds M for a sufficiently large n. Or in simpler terms, prove that n/(n+1) > M whenever n > N for some integer N.

I know that since the sequence goes to infinity, it can be seen as lim n→inf (n/(n+1)) is one, so I know that it's true, but how do I show that it's true?

Hint:

n/(n+1)

= (n + 1 - 1) / (n + 1)

= (n + 1) / (n + 1) - 1 / (n + 1)

Continue .......