It is given that \(\left(x+\frac{k}{x^2}\right)^n\) is a binomial expansion where \(k\) and \(n\) are positive constants.
Write down the first 4 terms in the expansion \(\left(x+\frac{k}{x^2}\right)^5\) in terms of \(k\).[2]
Hence, find the value of \(k\) if the term independent of \(x\) in the expansion \(\left(5x+\frac{3}{x^2}\right)\left(x+\frac{k}{x^2}\right)^5\) is 5.[3]
By using the formula for the general term, suggest two possible powers of \(n\) such that \(\left(x+\frac{k}{x^2}\right)^n\) contains a term independent of \(x\).[3]