Question

hey does anyone know if the following is convergent or divergent?? a(n)=( n/cos(n))
as n goes from 1 to infinity
plz help:)

Answer 1

If it's convergent \[\lim _{n \to \infty} {n \over \cos n} = L\]

Since the limit of n to infinity is either infinity or minus infinity in this case, it does not converge to some limit L and is divergent

Answer 2

thanks, that's really helpfull:)

Answer 3

also, does anyone know if the following are true or false:
(i) every sequence of real numbers is either bounded above or bounded below or both.
(ii) some convergent sequences are not bounded.

:)

Answer 4

what is the fourth term of the sequence

{max({0, (-2)^n})} as n goes from 1 to infinity

and i also need to know the sixth term of the sequence,
{min({0, (-2)^ (n+1) })} as n goes from 1 to infinity

thanks:)