# Prove Sequence is Convergent

• Feb 17th 2010, 04:39 PM
summerset353
Prove Sequence is Convergent
Use the definition of convergence to prove the sequence is convergent.
{(5n+17)/(2n)}

We have to prove the sequence converges to 5/2.
e>0, the n>= N
|[(5n+17)/(2n)] - [5/2]| = |17/(2(2n))|
There is where I am get stuck. I know we have to choose a postive integer N it is <e. Where do I go from here?
• Feb 17th 2010, 04:58 PM
Plato
Quote:

Originally Posted by summerset353
Use the definition of convergence to prove the sequence is convergent.
{(5n+17)/(2n)}

Here is a mistake. $\left| {\frac{{5n + 17}}{{2n}} - \frac{5}{2}} \right| = \frac{{17}}{{2n}}$.

So find a $N$ such that $\frac{{17}}{{2N}} < \varepsilon$.