- #1

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## Homework Statement

$$\lim_{x\to\infty} \left(\frac{n^2+2n+1}{n^2+2n+3}\right)^{\frac{2n^2}{n+1}}$$

## Homework Equations

3. The Attempt at a Solution [/B]

I tried

##\lim_{x\to\infty} \left(\frac{n^2+2n+3-2}{n^2+2n+3}\right)^{\frac{2n^2}{n+1}}=##

##\lim_{x\to\infty} \left(1+\frac{-2}{n^2+2n+3}\right)^{\frac{2n^2}{n+1}}=##

##\lim_{x\to\infty} \left(1 +\frac{-2}{n^2+2n+3}\right)^{\frac{n^2+2n+3}{-2}\frac{-2}{n^2+2n+3}\frac{2n^2}{n+1}}=##

##e^{\lim_{x\to\infty}\frac{-4n^2}{(n^2+2n+3)(n+1)}}=1##

and i get 1 but i dont think this is correct. My book gives ##e^2## as the solution. What do you think is wrong?