# Why is the output of my limit expression an interval?

Why is the output of the limit below an interval? It should be precisely $1$.

Limit[(2/Pi) ((2 n + 2)!!/(2 n + 1)!!) Integrate[(1 - x^2)^(n + 1/2), {x, 0, 1}],
n -> Infinity]
-

You have made an assumption without telling Mathematica about it. Namely, that $n$ is an integer. You can add this assumption like so: