Theorems · Theorem · number theory
Nat.geom_sum_le
∀ {b : ℕ}, 2 ≤ b → ∀ (a n : ℕ), ∑ i ∈ Finset.range n, a / b ^ i ≤ a * b / (b - 1)- Defined in
- Mathlib.Algebra.Order.Ring.GeomSum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.sumstatement and proof · cited by 5,195
- LE.le.transproof · cited by 3,151
- mul_commproof · cited by 2,262
- MulZeroClass.zero_mulproof · cited by 1,625
- Finset.rangestatement and proof · cited by 1,341
- tsub_pos_of_ltproof · cited by 31
- tsub_le_selfproof · cited by 22
- Finset.sum_range_zeroproof · cited by 9
- Nat.pred_mul_geom_sum_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.geom_sum_Ico_leproof · cited by 2