Determining a limsup value

Question

what is meant by 'lim sup' value? is it the convergence value of a sequence when $n$ goes to infinity?

What is the answer for, $$\limsup \left(\frac{4}{3n}\right)^{1/n}?$$ can someone help me please?

Answer 1

Lim sup and Lim inf are used to check whether sequence is converging or not. If Lim sup and Lim inf are same then sequence is converging.

Meaning of Lim sup and Lim inf : We can find Sup of any sequence, but it comes at some point, while lim sup gives what is sup value at infinity. Same with lim inf, it gives inf value at infinity. If both are same then sequence is converging.

Sequence which you have asked for is converging sequence at 1 (because $\lim{n\to\infty} (c/n)^{1/n} = 1$ where c: constant). So from that you can say that Lim sup is also 1.