Question

HELP PLASEPASE

Answer 1

@zepdrix

It says the answer is DNE.
I don't even know how they got that.

And SymboLab says otherwise...

Answer 2

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.

Answer 3

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

Answer 4

i dunno, the page doesn't go down that far lol

and im not sure if you get into subsequences at the calculus level.

Answer 5

I have no clue.

I mean isn't the fraction growing?
I dont think it alternates. :/

Answer 6

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.

\(\large\rm -1\le cos\frac{7bajillion}{5}\le 1\)

Answer 7

O. right.