(a) for what positive integers $n$ does $\left(x^2+\frac{1}{x}\right)^n$ have a nonzero constant term?

(b) for the values of $n$ that you found in part (a), what is that constant term? (you can leave your answer in the form of a combination.)

a. By the binomial theorem,

which produces a constant term when , or . is even for any choice of , so must be any positive integer for which is an even multiple of 3 i.e. a multiple of 6. Then can be any of the integers in the sequence {6, 12, 18, ...}.

b. Let for some positive integer . Then

and the constant term occurs when , or , or . At this value of , we get the term