# Find the limit of the sequence n^3/(2n^3 + n)

## Homework Statement

Find the limit for the following sequence and then use the definition of limit to justify your result.

n^3/(2*n^3 + n)

## The Attempt at a Solution

I found the limit as n --> infinity is 1/2. I think the next step is to set up the equation as follows:

n^3/(2*n^3 + n) = 1/2

But then I'm not sure if I should add n+1 to each side.

Dick
Homework Helper

Don't do any such thing. Look at the definition of a limit. Divide numerator and denominator of your expression by n^3. So you have 1/(2+1/n^2). Now you want to find an N for every epsilon such that n>N implies |1/(2+1/n^2)-1/2|<epsilon for any epsilon however small. Isn't that what the definition of limit said? Can you do that?

okay, I came up with 1/(2+1/n^2) which is where I came up the idea that the limit as n---->infinity is 1/2. But then if I set it to be < epsilon. How do you know what epsilon should be? I am really struggling with this concept. I appreciate your help and patience.

Dick