# Math Help - Convergence of infinite sequence of reals

1. ## Convergence of infinite sequence of reals

Let be an infinite sequence of reals. Show that if is convergent then we must have . If , must be convergent?

2. Originally Posted by Pythagorean12
Let be an infinite sequence of reals. Show that if is convergent then we must have . If , must be convergent?
What have you tried? Note that $\left|a_n-a_{n-1}\right|\le\left|a_n-L\right|+\left|a_{n-1}-L\right|$. For your second question, what about $a_n=n+\frac{1}{n}\implies a_{n}-a_{n-1}=\frac{1}{n}-\frac{1}{n-1}$?

3. Originally Posted by Pythagorean12
If , must be convergent?
You could try $a_n = \sqrt n$ or $a_n = \log n$.