Theorems · Theorem · sequences and series
sum_Ioo_inv_sq_le
∀ {α : Type u_1} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α] (k n : ℕ),
∑ i ∈ Finset.Ioo k n, (↑i ^ 2)⁻¹ ≤ 2 / (↑k + 1)- Defined in
- Mathlib.Analysis.PSeries
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
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
- LE.le.transproof · cited by 3,151
- Nat.cast_oneproof · cited by 2,501
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Finset.sum_congrproof · cited by 2,323
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- le_rflproof · cited by 1,558
- le_of_ltproof · cited by 1,175
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.sum_variance_truncation_leproof · cited by 1