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import TestGame.Metadata
import TestGame.Options.BigOperators
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
Game "TestGame"
World "Sum"
Level 4
Title "Summe aller ungeraden Zahlen"
Introduction
"
**Du**: Haben eigentlich alle Türme hier so kryptische Beschreibungen am Eingang?
Du gehst zu einem etwas kleineren Nachbarsturm.
"
set_option tactic.hygienic false
open BigOperators
Statement odd_arithmetic_sum
"$\\sum_{i = 0}^n (2n + 1) = n ^ 2$."
(n : ℕ) : (∑ i : Fin n, (2 * (i : ℕ) + 1)) = n ^ 2 := by
Hint "**Robo**: Das funktioniert genau gleich wie zuvor, viel Glück."