I'm reading Quantitative Portfolio Management by Isichenko, and one of the interview questions shared in the book is as follows:
Compute the products:
a. $\prod_{0 < i < j < \infty} (i^{1/i} - j^{1/j})$
b. $\prod_{0 < i < j < 2020} (i^{1/i} - j^{1/j})$
I am confused by this question. On first glance, I'd imagine that if $i=2$ and $j=4$, then since $\sqrt{2} = \sqrt[4]{4}$ then the entire product becomes zero in both cases.. Am I missing the point here?