Mathematical Induction & Proof Techniques

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1.
In the inductive step of mathematical induction, we assume P(k) is true and prove:
2.
Using mathematical induction, the formula 1 + 2 + 3 + ... + n = n(n+1)/2. For the base case n = 1, the LHS and RHS are:
3.
In the inductive step for 1 + 2 + ... + n = n(n+1)/2, assuming the formula holds for n = k, we need to show that 1 + 2 + ... + k + (k+1) equals:
4.
Prove by induction: 1^2 + 2^2 + ... + n^2 = n(n+1)(2n+1)/6. The base case n = 1 gives:
5.
In the principle of mathematical induction, the base case typically verifies the statement for:

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