# Evaluate this limit, introductory real analysis

1. May 14, 2012

### jaqueh

1. The problem statement, all variables and given/known data
limit of the sequence, [xn]=(-3n2+n+1)/(n2-2n+3)

2. Relevant equations
I so far know about the definition of a limit, squeeze principle, and lim[xnyn] = 0 if xn or yn goes to 0

3. The attempt at a solution
Tried the definition of the limit but the algebra got really crazy so i dont think i'm supposed to do it that way. I'm trying to squeeze it between (-3n2/n2) and (-3n3)/(n3), but i don't know if i can prove that the cubed one is greater than my sequence

2. May 14, 2012

### scurty

Try factoring out a variable of the highest power. This is a standard method for problems like these before l'Hospital's rule is introduced.

Edit: Just in case you aren't allowed to use that method..

If you want to use the squeeze theorem and then the definition of the limit, you need to factor out some terms by manipulating the original expression so they cancel out.

Last edited: May 14, 2012
3. May 14, 2012

### jaqueh

ah I've divided the numerator by 3 but am still stuck. I know it hits -3.

yeah I'm trying to see what I can make the expression into so things will start cancellong

4. May 14, 2012

### HallsofIvy

Staff Emeritus
Did you misunderstand what scurty said? Nothing about dividing by -3: factor out, or, same thing, divide both numerator and denominator by $n^2$.

5. May 14, 2012

### jaqueh

ok great I have it now. I do that then squeeze because I'm not allowed to say yet that 1/n goes to zero in a sequence I think