Rates of Convergence of Powers
Response to the following question:
Suppose that 0n=α+O(n-p)). Show that αn=α+O(n-q)).
Make a table listing h,h2,h3,and h4 for h=0.5,0.1,0.01, and 0.001, and discuss the varying rates of convergence of these powers of h as h approaches zero.
Provide step by step calculations.