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Question: Variable property and indexing?

Question:Variable property and indexing?

Alfred_F 315 Maple 2024
product
June 26 2025
1

On my journey of discovery through the world of Maple, I would like to ask for help again:
How are the properties of variables and the indexing of sequences handled/determined? For this purpose, I chose an old problem from a challenging MO as an exercise and tried it in the attached file, which, of course, failed.

restart

a[i] := 2*cos(t/2^i)-1

2*cos(t/2^i)-1

 (1)

b[n] := product(a[i], i = 1 .. n)

product(2*cos(t/2^i)-1, i = 1 .. n)

 (2)

limit(b[n], n = infinity)

limit(product(2*cos(t/2^i)-1, i = 1 .. n), n = infinity)

 (3)

simplify(limit(b[n], n = infinity))

limit(product(2*cos(t*2^(-i))-1, i = 1 .. n), n = infinity)

 (4)

NULL

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