hmm okay

thanks for the replies!

unfortunately I have more questions...

say if a sequence a_n converes to a, and a_n > 1 for all n >=1, show that a>=1

It's obvious right? if it's a sequence say (n+1)/n, it's always bigger than 1 and it's limit is 1 but how do i show it?

a sequence (cos n )/ (2 - sin n ) is bounded right?

it does not converge or is monotone right?

just want to clarify :

the question is find a Cauchy sequence such that it is rational for all n bigger or equals to 1 such that its limit is not rational.

was thinking about [(n+1)/n]^n

its limit is e and its not rational right?

but is it the sequence rational?