Limit problem

[Hermitage]

Hello again!

I have trouble finding a limit of this:
((n^2)+((-1)^n)*n)/(1-2*n^2)

. . . . .\(\displaystyle \displaystyle{\lim_{n\, \rightarrow \, \infty}\, \frac{(-1)^n\, n\, +\, n^2}{1\, -\, 2n^2}\, =\, -\frac{1}{2}}\)

the problem is that i get the same answer as is shown above. But the book says the answer should be -1/3
Is my answer correct?

 

[Quaid]

i get [-1/2, but] the book says the answer should be -1/3

Is my answer correct?

Your answer is correct!

 

[HallsofIvy]

I agree. If the problem is as you say, then the limit is -1/2 not -1/3. Perhaps a simple misprint.

Dividing both numerator and denominator by \(\displaystyle n^2\), the highest power of n in the fraction, you get \(\displaystyle \frac{(-1)^n(1/n)+ 1}{1/n^2- 2}\). Taking the limit as n goes to infinity, each fraction with an n in the denominator goes to 0, leaving \(\displaystyle -\frac{1}{2}\).

 

[Hermitage]

Wohoo.
Thanks guys!