Theorems · Theorem · real analysis
geom_sum_Ico_le_of_lt_one
∀ {K : Type u_1} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K] {x : K} {m n : ℕ},
0 ≤ x → x < 1 → ∑ i ∈ Finset.Ico m n, x ^ i ≤ x ^ m / (1 - x)- Defined in
- Mathlib.Algebra.Order.Field.GeomSum
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- Finset.sumstatement and proof · cited by 5,195
- IsStrictOrderedRingstatement and proof · cited by 2,490
- LT.lt.leproof · cited by 2,189
- le_rflproof · cited by 1,558
- LT.lt.neproof · cited by 872
- Finset.Icostatement · cited by 450
- le_or_gtproof · cited by 269
- sub_posproof · cited by 147
- pow_nonnegproof · cited by 141
Cited by1
Results whose statement or proof uses this declaration.
- sum_div_pow_sq_le_div_sqproof · cited by 1