Asked to compute:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\lim_{n\to\infty} (-1)^nsin(1/n)

[/tex]

I've broken this limit down into:

[tex]

\lim_{n\to\infty} (-1)^n * \lim_{n\to\infty}sin(1/n)

[/tex]

I've determined [tex] \lim_{n\to\infty}sin(1/n) = 0[/tex]

Now I have [tex] \lim_{n\to\infty} (-1)^n * 0[/tex]

This is where I run into trouble...

Attempting to solve for [tex] \lim_{n\to\infty} (-1)^n [/tex]:

-I've tried plugging in integers and rational numbers for n. It jumps to -1 and 1 with integers, and spits out complex numbers when I plug in rational numbers.

-I've also tried graphing this function on a calculator to no avail.

-I've also plugged it into maple and it spits out: (-1..1).

Is it safe to say [tex] \lim_{n\to\infty} (-1)^n [/tex] does not exist?

In which case, I have something that does not exist multiplied by 0, and anything multiplied by 0 equals 0... but I have "nothing" not "anything" ;)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Simple Limit

**Physics Forums | Science Articles, Homework Help, Discussion**