We have just been introduced to infinite series of functions, and immediately started working on uniform convergence and Weierstrass' M-test, and how the sum of the series behaves in terms of integration, differentiation, etc.
But what about 'pointwise' convergence of a series of functions, like we had for sequences? What's the definition for that? Do I simply pick and $x$, and show that the series I get (which is one of numbers $a_n$) is convergent, or is there more to it?
