I am reading Principles Of Mathematical Analysis by Walter Rudin. Chapter 8, Equation 28 needs some clarification. We are taking a lim as h->0 on a series. Value of series is lim as n->INF on the squence of partial sums. So first we take lim as n->INF on a sequence of partial sums and then we are taking lim as h->0. But can we interchange the order of limits. If so result is immediate. But how to prove that we can change the order of limits? Is it that we have to use Thearem 7.11? Please help me.