no goals
α : Type u
inst✝ : Semiring α
⊢ ∑ i in range 0, 0 ^ i = if 0 = 0 then 0 else 1
simp
no goals
α : Type u
inst✝ : Semiring α
⊢ ∑ i in range 1, 0 ^ i = if 1 = 0 then 0 else 1
simp
α : Type u
inst✝ : Semiring α
n : ℕ
⊢ 0 ^ (n + 1) + ∑ i in range (n + 1), 0 ^ i = if n + 2 = 0 then 0 else 1
α : Type u
inst✝ : Semiring α
n : ℕ
⊢ ∑ i in range (n + 2), 0 ^ i = if n + 2 = 0 then 0 else 1
rw [geom_sum_succ']
no goals
α : Type u
inst✝ : Semiring α
n : ℕ
⊢ 0 ^ (n + 1) + ∑ i in range (n + 1), 0 ^ i = if n + 2 = 0 then 0 else 1
simp [zero_geom_sum]