Prove sum of first n integers formula by induction
Analyze the prove sum of first n integers 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 first n integers formula (S(n) = n(n+1)/2) and verify it for n=1.
Assume the formula holds for some arbitrary positive integer k (inductive hypothesis), then express S(k+1) in terms of S(k) and simplify to match the formula for n=k+1.
Identify the critical step in the inductive proof where the assumption for k is used to establish the case for k+1, and explain why this step is essential for the proof's validity.
Prove sum of first n integers formula by induction
Analyze the prove sum of first n integers formula by induction.