HELP PLASEPASE

Question

HELP PLASEPASE

itz_sid · Answer

@zepdrix 

It says the answer is DNE.
I don't even know how they got that.

And SymboLab says otherwise...

zepdrix · Answer

Well remember when we had that alternating business in the last problem? We didn't have a problem because the sequence was approaching 0 the larger that n got.

That isn't happening here,
we just cycle endlessly through different cosine values.
Never converging to any specific one though.

zepdrix · Answer

Oh they do something fancy to prove this though?
Looking at subsequences or something?

zepdrix · Answer

i dunno, the page doesn't go down that far lol

and im not sure if you get into subsequences at the calculus level.

itz_sid · Answer

I have no clue.

I mean isn't the fraction growing?
I dont think it alternates. :/

zepdrix · Answer

Well we know the limits of cosine, right?

$\large\rm -1\le cos\frac x5\le 1$

It will never get larger or smaller than those end values.
Doesn't matter how humongous the fraction gets.

$\large\rm -1\le cos\frac{7bajillion}{5}\le 1$

itz_sid · Answer

O. right.