Product Expansion - MaplePrimes

Question:Product Expansion

Posted: digerdiga 390 Product: Maple 2018

July 24 2018

The following product gives 0

restart;

product(1-1/k, k = 2 .. infinity);

However when I expand the product

1 - 1/2 - 1/3 - 1/4 - ... + 1/2*1/3 + 1/2*1/4 + ... + 1/3*1/4 + ... + triple products + quadruple products + and so forth...

Now the double, triple, quadruple, and so forth sums of products converge.

The 1/2 + 1/3 + 1/4 + ... nevertheless diverges, so why does maple give me 0?

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