Principle of mathematical induction and applications.
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Q1 · Mathematical Induction · MEDIUM
The statement 2ⁿ > n is true for all natural numbers n by mathematical induction. The base case n = 1 gives
Q2 · Mathematical Induction · EASY
Using mathematical induction, 1 + 2 + 3 + ... + n equals
Q3 · Mathematical Induction · HARD
If 1² + 2² + 3² + ... + n² = n(n + 1)(2n + 1)/6 is assumed true for n = k, then the sum 1² + 2² + ... + k² + (k + 1)² equals