Theorems · Theorem · sequences and series
tsum_geometric_of_lt_one
∀ {r : ℝ}, 0 ≤ r → r < 1 → ∑' (n : ℕ), r ^ n = (1 - r)⁻¹- Defined in
- Mathlib.Analysis.SpecificLimits.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- SummationFilter.unconditionalstatement · cited by 2,068
- tsumstatement · cited by 1,148
- HasSum.tsum_eqproof · cited by 150
- hasSum_geometric_of_lt_oneproof · cited by 14
Cited by6
Results whose statement or proof uses this declaration.
- Real.ofDigits_le_oneproof · cited by 3
- Complex.tendsto_tsum_powerSeries_nhdsWithin_stolzSetproof · cited by 2
- hasSum_two_pi_I_cauchyPowerSeries_integralproof · cited by 2
- Real.ofDigits_const_last_eq_oneproof · cited by 1
- LiouvilleNumber.remainder_lt'proof · cited by 1
- Cardinal.increasing_cantorFunctionproof · cited by 1