Stefani_problem_stefani_problem -

Finding a single case where a statement fails to disprove it. 3. Application: The Fibonacci Identity

∑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: stefani_problem_stefani_problem

In the De Stefani curriculum, problems are designed to test five fundamental proof techniques: Finding a single case where a statement fails to disprove it

fkfk+1+fk+12=fk+1(fk+fk+1)f sub k f sub k plus 1 end-sub plus f sub k plus 1 end-sub squared equals f sub k plus 1 end-sub of open paren f sub k plus f sub k plus 1 end-sub close paren by definition: fk+1fk+2f sub k plus 1 end-sub f sub k plus 2 end-sub The identity is proven for all Resources for Further Study stefani_problem_stefani_problem

Directly building an example that satisfies the property.