Question Detail

MTH 101 MTH 101 Past Questions Objective Question
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Question

Which of the following cannot be proved by induction?
Options
A 1²+2²+...+n² = n(n+1)(2n+1)/6
B The sum of all angles in a triangle is 180°
Correct Answer
C 2ⁿ > n for all n ≥ 1
D 2ⁿ > n² for n ≥ 4
Correct Answer

Option B is the correct answer.

Detailed Explanation

Mathematical induction is used to prove statements about natural numbers. The sum of angles in a triangle is a geometric fact that holds for all triangles, but it's not a statement indexed by natural numbers in a way that induction can be applied directly.

Hint

Induction is typically used for statements involving natural numbers.

Question Info

Course: MTH 101
Topic: MTH 101 Past Questions
Type: Objective
Difficulty: Not specified
Question 402 of 696
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