Question

I need help finding the limit of the following sequence or determining that the limit does not exists

{csc^(-1) 11n}

Answer 1

well, consider that 11n just gets bigger and bigger without bound.

csc(x) has an asymptote at x = π
That is, csc(x) -> ∞ as x -> π
So, csc^1(x) -> π as x -> ∞

Or, in the case of our sequence,

lim {csc^(-1) 11n} = π
n->∞