# Thread: Limits: True, or false?

1. ## Limits: True, or false?

By choosing one word within each parentheses, four statements can be made from the following. Which are false (give counterexample) and which are true?

If Lim $a_{n}$ is (positive, non-negative), then for large n the individual terms $a_{n}$ are (positive, non-negative).

2. Originally Posted by cgiulz
By choosing one word within each parentheses, four statements can be made from the following. Which are false (give counterexample) and which are true?

If Lim $a_{n}$ is (positive, non-negative), then for large n the individual terms $a_{n}$ are (positive, non-negative).
Theorem: If the limit of a sequence is positive then almost all the terms of the sequence are positive.
The limit of $\left( {\frac{{\left( { - 1} \right)^n }}{n}} \right)$ is non-negative.