The J-function is a cohomology valued function, defined for any symplectic manifold, which captures information about (descendent) Gromov-Witten invariants. Gamma Conjecture 1, proposed by Galkin, Golyshev and Iritani, states that a (normalised) limit of the J-function yields the Gamma class (a certain characteristic class). In this talk I will give a quick introduction to the J-function and the Gamma class. Then I will explain how one can sometimes use results about power series to reduce Gamma Conjecture 1 to a simpler statement. For projective spaces, this leads to an easy proof of the conjecture.