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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 4
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Title "Bernoulli Ungleichung"
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Introduction
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"
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Hier nochmals eine Übung zur Induktion.
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"
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open BigOperators
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Statement
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"Zeige folgende Gleichung zur Summe aller ungeraden Zahlen:
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$\\sum_{i = 0}^n (2n + 1) = n ^ 2$."
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(n : ℕ) : (∑ i : Fin n, (2 * (i : ℕ) + 1)) = n ^ 2 := by
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induction' n with n hn
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simp
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rw [nat_succ]
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sorry -- waiting on Algebra.BigOperators.Fin
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--simp [Fin.sum_univ_cast_succ]
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--rw [hn]
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--ring
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Tactics ring
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