# Analysis: What is the relationship between the infinite triple series and the sum of the same sequence in some order?

Leave $$a_ {i, j, k}$$ Be a sequence of real numbers. Fix a bijection $$f: mathbb {N} rightarrow mathbb {N} ^ {3}$$. Define the sequence $$b_ {n}$$ as $$b_ {n} = a_ {f (n)}$$. So if the series $$sum b_ {n}$$ converge, and the iterated sum of $$sum_ {i} ^ { infty} sum_ {j} ^ { infty} sum_ {k} ^ { infty} a_ {i, j, k}$$ converge

What is the relationship between the two? (the same question for a sequence on any number of indexes)