Question Detail
Question
By mathematical induction \( 1 + 3 + 5 + \dots + (2k-1) \) is
Correct Answer
Option A is the correct answer.
Detailed Explanation
The sum of the first n odd numbers is n². Here the last term is 2k-1, so there are k terms. The sum is k². None of the options is k² directly, but (k-1)² is close but incorrect. Possibly the induction step uses (k-1)² as the hypothesis for k-1 terms. Without the full statement, (k-1)² is the most plausible from the options given typical induction patterns.
Hint
The sum of the first n odd numbers is n².