Thanks, Alex. This did the trick, and I figured it out in a breeze.However...
...when I naively tried to exptrapolate the idea to a variant of this sequence, I failed.
This time, I used "2" as the numerator of the second term:
(1 - 2/4 ) · (1 - 2/9) · (1 - 2/16) · ... · (1 - 2/nē) = ?
In the first sequence, because of the nice properties of the number 1, this doesn't become obvious, but if you try the same technique, you first rush to a quadratic like so:
1st seq.: 1 - (1/nē) = (nē - 1)/nē = ((n - 1) · (n + 1))/nē
2nd seq.: 1 - (2/nē) = (nē - 2)/nē = ((n - sqrt(2)) · (n + sqrt(2)))/nē
Unfortunately, the terms do not cancel each other this time. (And/or I simply do not have the *algebraic imagination* to express this in a way that'll be conducive to that technique -- a greater possibility ;)).
I didn't want to spend hours in trial-and-error with complex numbers so I came back -- to ask for you to kindly suggest material (on this or other sit's)discussing this issue in further detail.
--
BTW Alex, I absolutely LOVED cut-the-knot.org. Fantastic site! It's been such a pleasure for someone like me (a 40-something math-challenged enthusiast) to discover it. Congratulations! :)
Cheers
KE