- #1

Potatochip911

- 318

- 3

## Homework Statement

$$\lim_{x\to\infty} \dfrac{(-1)^n\sqrt{n+1}}{n}$$

## Homework Equations

3. The Attempt at a Solution [/B]

This is what I managed to do but I just wanted to verify that this is the correct way of solving it, I'm mainly concerned about the fact that I took the absolute value with the log function, is that a valid operation?

$$y=\lim_{x\to\infty} \dfrac{(-1)^n\sqrt{n+1}}{n} $$

$$ \ln y=\lim_{x\to\infty} \ln|\dfrac{(-1)^n\sqrt{n+1}}{n}| $$

$$ \ln y=\lim_{x\to\infty} \ln|\dfrac{(-1)^n\sqrt{n+1}}{n}| $$

$$\ln y=\lim_{x\to\infty} \ln|(-1)^n|+\lim_{x\to\infty} \ln|\dfrac{\sqrt{n+1}}{n}|$$

$$\ln y=\lim_{x\to\infty} \dfrac{\ln|1|}{n^{-1}}+\lim_{x\to\infty} \ln|{\sqrt{1/n+1/n^2}}|$$

$$\ln y=\lim_{x\to\infty} \dfrac{0}{n^{-2}}+ \ln|0|$$

$$\ln y=-\infty$$

$$y=e^{-\infty}$$

$$y=0$$