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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?

enter image description here

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    Of course not (That is, you are right!). Please put a screenshot of the Wolfram Alpha result, along with your input, so that we can decide what's the problem. – 2017-01-31
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    Don't see that [here](http://www.wolframalpha.com/input/?i=lim+(5%2F3)%5En+for+n+to+infinity). It helped if you posted the exact text you typed into WA. – 2017-01-31
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    I am trying to post a screenshot, but I don't know how to do it – 2017-01-31
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    @ChristianAndrews `as long as n increases` Read the screen more carefully. What's $0$ is the limit for $n \to -\infty\,$ which is of course correct. – 2017-02-01
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    oh man, sorry about that, You're right, I was wrong – 2017-02-01
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    Limits don't go anywhere. They either exist or don't, but they're not moving around to a samba beat. – 2017-02-01
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    To expand on what @zhw. said: The standard terminology goes something like, "as $x$ goes to $c$, the value $f(x)$ goes to $L$". That is, it's the dependent and independent variables ($x$ and $y$) that do the going, not the limit ($L$). – 2017-02-01

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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:

limit n to infinity (5/3)^n

lim_{n to infinity} (5/3)^n

And they both gave me the correct answers.

What I suspect you've done is this:

limit n to infinity 5/3^n

lim_{n to infinity} 5/3^n

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.

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    Look closely: $n \to -\infty$. – 2017-02-01
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    As zhw said in another comment, limits don't go anywhere. So I think you should not use that kind of phrasing as it misleads students. – 2017-02-01
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I suspect you are missing a pair of parentheses: If you type

Limit[5/3^n, n -> Infinity]

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

Limit[(5/3)^n, n -> Infinity]

you will get your intended result, which is $$\lim_{n \to \infty} \left(\frac{5}{3}\right)^n = \infty.$$

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    Occam's razor agrees. – 2017-01-31
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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.

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This sequence definitely approaches infinity as $n$ goes to infinity.

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    so, It could be a wolframalpha's mistake? because I trust in wolfram blind eye – 2017-01-31
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    My guess is that you forgot a parenthesis or input the limit incorrectly into Wolfram. – 2017-01-31
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    When I enter it into Wolfram Alpha, the limit comes back as infinity. – 2017-01-31