Mathlib Map

Theorems · Theorem · sequences and series

summable_one_div_pow_of_le

∀ {m : ℝ} {f : ℕ → ℕ}, 1 < m → (∀ (i : ℕ), i ≤ f i) → Summable fun i => 1 / m ^ f i

A series whose terms are bounded by the terms of a converging geometric series converges.

Defined in
Mathlib.Analysis.SpecificLimits.Basic
Cited by
2 results in Mathlib
Foundations
Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites24

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.