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)