Limit goes to $\infty$, but wolfram alpha says its limit is $0$
Mia Lopez 
I have $(5/3)^n$, if I input this in wolframalpha.com I can see it goes to infinity as long as n increases, but if I go down in the wolframalpha webpage results it shows .... the limit is zero as long as n increases, am I wrong?
4 Answers
$\begingroup$As you've correctly said, the value of the limit approaches $\infty$ as $n \to \infty$.
I typed the limit into Wolfram|Alpha using these inputs:
And they both gave me the correct answers.
What I suspect you've done is this:
Which is $\lim_{n \to \infty} \frac{5}{3^n}=0$ instead of the correct limit $\lim_{n \to \infty} \left(\frac{5}{3}\right)^n=\lim_{n \to \infty} \left(\frac{5^n}{3^n}\right)=\infty$
Edit: After you provided the screenshot:
Look carefully at the input given by Wolfram Alpha on your screenshot.
$$\lim_{\color{red}{n \to -\infty}} \left(\frac{5}{3}\right)^n=0$$
The limit tends to $-\infty$ instead of $+\infty$.
To avoid this problem in the future: Type the limit explicitly rather than just typing $(\frac{5}{3})^n$ on Wolfram|Alpha as I have done on my top two examples.
$\endgroup$ 2 $\begingroup$I suspect you are missing a pair of parentheses: If you type
You will get 0, because the order of operations makes this equivalent to $$\lim_{n \to \infty} \frac{5}{3^n} = 0.$$ If you type
you will get your intended result, which is $$\lim_{n \to \infty} \left(\frac{5}{3}\right)^n = \infty.$$
$\endgroup$ 1 $\begingroup$You said down the page was a limit of 0. That's because they took $n -> -\infty$. Edit OP shows the same thing circled on screen print.
$\endgroup$ $\begingroup$This sequence definitely approaches infinity as $n$ goes to infinity.
$\endgroup$ 3
