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import TestGame.Metadata
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import Mathlib.Tactic.Ring
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import Mathlib
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import TestGame.ToBePorted
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Game "TestGame"
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World "Induction"
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Level 5
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Title "Bernoulli Ungleichung"
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Introduction
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"
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TODO: Induktion (& induktion vs rcases)
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"
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example (x : ℕ) (n : ℕ) : 1 + n * x ≤ (x + 1) ^ n := by
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induction' n with n hn
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simp
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rw [Nat.succ_mul]
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rw [Nat.pow_succ]
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sorry
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example (n : ℕ) : (∑ i : Fin (n + 1), ↑(2 * i - 1)) = n ^ 2 := by
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induction' n with n hn
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simp
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Statement
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"Zeige $\\sum_{i = 0}^n i = \\frac{n ⬝ (n + 1)}{2}$."
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(n : ℕ) : (∑ i : Fin (n + 1), ↑i) = n * (n + 1) / 2 := by
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apply hh1
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induction' n with n hn
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simp
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sorry
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-- rw [Fin.sum_univ_castSucc]
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-- simp [nat_succ]
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-- rw [mul_add, hn]
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-- ring
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Tactics ring
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