Theorems · Theorem · ring theory
geom_sum_succ
∀ {R : Type u_1} [inst : Semiring R] {x : R} {n : ℕ},
∑ i ∈ Finset.range (n + 1), x ^ i = x * ∑ i ∈ Finset.range n, x ^ i + 1- Defined in
- Mathlib.Algebra.Ring.GeomSum
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Finset.sumstatement and proof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- Finset.rangestatement and proof · cited by 1,341
- pow_zeroproof · cited by 1,094
- Finset.mul_sumproof · cited by 196
- Finset.sum_range_succ'proof · cited by 37
Cited by5
Results whose statement or proof uses this declaration.
- geom_sum_alternating_of_lt_neg_oneproof · cited by 2
- geom_sum_alternating_of_le_neg_oneproof · cited by 1
- geom_sum_pos_and_lt_oneproof · cited by 1
- Ideal.index_pow_leproof · cited by 0
- IteratedWreathProduct.cardproof · cited by 0