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MTH 101 MTH 101 Past Questions Objective Question
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Question

One of the following is a necessary step for proving 1+3+5+...+(2n-1) = n²?
Options
A verify for n = k
B Assume 1+3+...+k is true and prove for P(k+1)
C Prove that n = 1 is true
Correct Answer
D prove that for 1+3+...+2k+1 = (k+1)²
Correct Answer

Option C is the correct answer.

Detailed Explanation

For mathematical induction, we must first verify the base case (n=1). The left side when n=1 is 1, and the right side is 1²=1, so the statement holds for n=1, establishing the base case before proceeding with the inductive step.

Hint

Mathematical induction requires both a base case and an inductive step.

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 361 of 696
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