Using principle of mathematical induction prove the following

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1. Use the Principle of Mathematical Induction to prove that 2 | (n2 − n) for all n ≥ 0.
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2. 1. Prove that 12 + 22 + 32 + ⋯ + 𝑛𝑛2 = 𝑛𝑛(𝑛𝑛+1)6(2𝑛𝑛+1) , ∀𝑛𝑛 ∈ ℕ by using the principle
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3. 1. Prove that 1^2+ 2^2+ 3^2 + ⋯ + 𝑛^2 = 𝑛(𝑛+1)(2𝑛+1)÷6, ∀𝑛𝑛 ∈ ℕ by using the principle ofmathematical
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4. Prove by Principle of Mathematical Induction that for every positive integersn , 3^n >n^2
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