Integral approximation and nim strategy

Question

Assignment:

Q1. Two players take turns removing 1, 2, 3, or 4 objects from a set of 16 identical objects (without replacing them.) The winner is the player who removes the last object. Find a winning strategy for one of the players (the one who plays first or second).

Q2. If a and b are both greater than -1, find the  lim_(n→∞)?n^(b-a)  (1^a+2^a+?+n^a)/(1^b+2^b+?+n^b).

Provide complete and step by step solution for the question and show calculations and use formulas.