Prove sum of squares formula by induction
Analyze the prove sum of squares formula by induction.
Examples
Input: "proof_case_1"
Output: true
Input: "proof_case_2"
Output: true
Hints
Recall the base case for the sum of squares formula (n=1) and verify it holds true.
Assume the formula holds for some arbitrary positive integer k (induction hypothesis), then express the sum of squares up to (k+1) in terms of the sum up to k.
Using the induction hypothesis, algebraically manipulate the expression for the sum up to (k+1) to show it matches the formula with (k+1) substituted for n, thereby completing the induction step.
Prove sum of squares formula by induction
Analyze the prove sum of squares formula by induction.