Question

Lim n --> Infinity of (-1)^(n/7)
I think this has to do with geometric series, but I don't know how

Answer 1

I don't know either, but I am going to graph plot the equation and see what happens as n gets very very large.

Can you check my work for me?

Answer 2

but if you plot graph what you get (-1)^infinity

Answer 3

what dose it mean in graph

Answer 4

i think this was has no solution

Answer 5

what do you say

Answer 6

and even it happens this question was not exist,

Answer 7

Sorry my OS locked up. I agree with you but that is happen I am trying to figure out.

Answer 8

but how

Answer 9

liten bro the quetion asker was gonne how we can know the question was real or from middle of the any solution

Answer 10

Sorry OS issue I had to change computers.

Answer 11

Did you tried it yet.

Answer 12

Yo bro where did you go?

Answer 13

I need to Google limits of negative numbers raised to powers.

Bye

Answer 14

\(\color{#000000 }{ \displaystyle \lim_{n\to\infty}(-1)^{n/7} }\)

I am not going to solve this completely, but I will try to give you a good demonstration of this limit. This should be helpful ...

Ok, let's go:)

\(\large\color{black}{ \large{ \begin{array}{| l | c | r |}
\hline ~~~n~~~~ & \displaystyle \lim_{n\to\infty}(-1)^{n/7} \\
\hline
~~~70,000~ & \displaystyle (-1)^{70,000/7} =(-1)^{10,000}=\color{blue}{1} \\
\hline
\scr~~~70,007~ & \displaystyle (-1)^{70,007/7} =(-1)^{10,001}=\color{blue}{-1} \\
\hline
\scr~~~70,014~ & \scr \displaystyle (-1)^{70,014/7} =(-1)^{10,002}=\color{blue}{1} \\
\hline
\scr~~~70,021~ & \scr \displaystyle (-1)^{70,021/7} =(-1)^{10,003}=\color{blue}{-1} \\
\hline
\rm so~on~... & \rm~See~the~pattern? \\
\end{array} } }\)

Answer 15

The idea is that you can go infinitely on and on, and your "output" (or the "general term") is not approaching a single value.

Remember that for a limit to exist it has to approach ONE value (not multiple values).

e.g.
A two-sided limit must approach same (and numerical, not \(\infty)\) value from both sides.
OR, any one-sided limit must approach one numerical value. If it alternates between +3 or -3 for example, or if it just goes to positive or negative infinity, then it does not exist.

Answer 16

You can easily make sense, just by using the "English" definition.
Limit - means that some quantity is given a limit.

This means that it is not infinitely large (\(+ \infty\)), or infinitely small (\(- \infty\)). Then it is not "limited", rather, it is unbound, or "u nlimited, if you will.

And that also means that there is a single (one) limit to some quantity. (i.e. it doesn't "alternate" - or, doesn't approach many numbers at once.