Theorems · Theorem · sequences and series

Summable.sum_add_tsum_nat_add

∀ {G : Type u_2} [inst : AddCommGroup G] [inst_1 : TopologicalSpace G] [IsTopologicalAddGroup G] [T2Space G] {f : ℕ → G}
  (k : ℕ), Summable f → ∑ i ∈ Finset.range k, f i + ∑' (i : ℕ), f (i + k) = ∑' (i : ℕ), f i

Defined in

Mathlib.Topology.Algebra.InfiniteSum.NatInt

Cited by

6 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupTopologicalSpaceIsTopologicalAddGroupT2Space