Nested Summations

As it happens, Fibonacci numbers can be expressed as finitely nested finite sums. And likewise, numbers in Fibonacci sequences that start with natural numbers other than 0 and 1, e.g., Lucas numbers, can be expressed as finitely nested finite sums as well. This article also shows how to also express Jacobstahl numbers as finitely nested finite sums. The construction scales to Jacobstahl sequences with a core multiplicative factor other than the standard one. All of this ought to keep Jens entertained (or at least busy) in one of his legendary proof sessions with his students.