Solve the function step-by-step. Then Does the sequence converge, or diverge? (-1)^(n-1)/sqrt(n)

Question

anonymous · Answer

@halorazer Any ideas?...Im done..My brain is gone :/

zzr0ck3r · Answer

what does solve a function mean?

zzr0ck3r · Answer

$\frac{(-1)^{n-1}}{\sqrt{n}}$?

anonymous · Answer

It just means(show the steps) solve it. lol

anonymous · Answer

And yes that is how the problem is set up. :)

zzr0ck3r · Answer

$-1\le(-1)^{n-1}\le 1$
so

$\frac{-1}{\sqrt{n}}\le\frac{(-1)^{n-1}}{\sqrt{n}}\le\frac{1}{\sqrt{n}}$
now let $n\rightarrow \infty$
$0\le\frac{(-1)^{n-1}}{\sqrt{n}}\le 0$
so 
$\lim_{n\rightarrow \infty}\frac{(-1)^{n-1}}{\sqrt{n}}=0$

anonymous · Answer

So basically it converges?

zzr0ck3r · Answer

if you are asking that question I have a feeling you are confused. which part are you confused about.

zzr0ck3r · Answer

yes it converges to 0

anonymous · Answer

Thank you so much! :) It makes sense now, I got an answer similar but I couldn't figure out why 0 converged...I was making such a big(small) mistake. Haha now I can rest. :P