Question

Is this sequence convergent or divergent? I don't really see either nor monotone.

Answer 1

\[a_n = \cos(n \pi/2)\]

math questions account xD

@ganeshie8

Answer 2

It's bounded between -1 and 1, so it's not monotone...

Answer 3

But is it convergent then, because of the bounds, mhm.

Answer 4

since the limit is DNE
the sequence is divergent

Answer 5

OH

Answer 6

Yeah i just drew out the graph as well lol, to make sure what the heck is going on

Answer 7

it flip flops between 1 and -1 i guess

Answer 8

I remember reading another one similar to this I think it was \[a_n =(-1)^n\] so this one would also flip flop right? So therefore it's divergent as it doesn't exist either.

Answer 9

\[\left\{ -1,1,-1,1,-1... \right\}\]