Stefani_problem_stefani_problem -

This property is closely related to the , which is often used to optimize dynamic programming algorithms from 2. Fundamental Proof Techniques

You can find similar problems archived on CliffsNotes under Lorenzo De Stefani’s course materials. stefani_problem_stefani_problem

∑i=1k+1fi2=(∑i=1kfi2)+fk+12sum from i equals 1 to k plus 1 of f sub i squared equals open paren sum from i equals 1 to k of f sub i squared close paren plus f sub k plus 1 end-sub squared Substitute the inductive hypothesis: This property is closely related to the ,

Proving a base case and showing the property holds for if it holds for Inductive Step: Assume the formula holds for

of real numbers is defined as a if, for all indices , the following inequality holds:

In the De Stefani curriculum, problems are designed to test five fundamental proof techniques:

∑i=1nfi2=fnfn+1sum from i equals 1 to n of f sub i squared equals f sub n f sub n plus 1 end-sub Step-by-Step Induction Proof .The base case holds. Inductive Step: Assume the formula holds for . We must show it holds for