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GIKI Practice Maths Mathematical Induction MCQs Test 2
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GIKI Practice Maths Mathematical Induction MCQs Test 2

Practice GIKI 2026 Practice Test Maths MCQs from Mathematical Induction. Get instant results with Explanation.
Practice Quiz 2 for "Mathematical Induction" (Maths). Total 31 MCQs available, split into 4 quizzes. Test your understanding of core concepts. Mastering these concepts is essential for securing a high percentile in GIKI.
General10 MCQs
1. Which of the following is a necessary step in proof by induction?
2. If P(k) is true, and we prove P(k) ⇒ P(k+1), then by induction P(n) is true for all n ≥ 1. This is the principle of:
3. The sum of cubes of first n natural numbers is:
4. Using induction, to prove 1² + 2² + ... + n² = n(n+1)(2n+1)/6, the inductive step adds:
5. The base case for proving 2ⁿ ≥ n² for n ≥ 4 is:
General10 MCQs
6. If we prove P(1) and P(k) ⇒ P(k+1), we can conclude P(n) is true for:
7. The statement 1 + 3 + 5 + ... + (2n-1) = n² is proven by induction. The base case is n = 1, LHS=1, RHS=1. In the inductive step, the sum for n=k+1 becomes:
8. For the inequality 2^n > n for all n ≥ 1, the inductive step shows that 2^(k+1) > k+1 using the assumption 2^k > k. How?
9. The sum 1 + 2 + 4 + ... + 2^{n-1} equals:
10. To prove that 3 divides n³ - n for all natural numbers n, induction is used. The base case n=1 gives 1³-1=0, divisible by 3. In the inductive step, we add:

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