Cogito Ergo Sum (ii)

Let's try something different. Show that

            1       1         1
(1)       ----- - ----- < ---------
          1,000   1,001   1,000,000

Cogito Ergo Sum.

Two persons are credited with the quotes below. One is very well-known among economists -- amateurs and professionals, alike -- the other is better-known among philosophers and logicians.

Person A is quoted variously as saying:

"I don't need algebra, I can think."

or, in an alternative version:

"I never learned math, so I had to think."

Person B:

"Few persons care to study logic, because everybody conceives himself to be proficient enough in the art of reasoning already. But I observe that this satisfaction is limited to one's own ratiocination, and does not extend to that of other men."

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