Question

Let \( T(k) \) be the statement \( 1 + 3 + 5 + \dots + (2k - 1) = k^2 + 10 \). Which of the following is correct?

• A. \( T(1) \) is true
• B. \( T(k) \) is true \( \Rightarrow T(k+1) \) is true
• C. \( T(k) \) is true for all \( n \in N \)
• D. All above are correct

Hint:

Mathematical induction is a powerful tool for proving statements that hold for all natural numbers.

Answer 1

The Correct Option is B

Step 1: Mathematical induction.
This is a problem of mathematical induction. We prove that if \( T(k) \) is true, then \( T(k+1) \) is true.
Thus, the correct answer is (2).