Theorems · Theorem · sequences and series

hasSum_nat_add_iff

∀ {G : Type u_2} [inst : AddCommGroup G] {g : G} [inst_1 : TopologicalSpace G] [IsTopologicalAddGroup G] {f : ℕ → G}
  (k : ℕ), HasSum (fun n => f (n + k)) g ↔ HasSum f (g + ∑ i ∈ Finset.range k, f i)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.NatInt

Cited by

6 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupTopologicalSpaceIsTopologicalAddGroup