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THUDandBLUNDER · Threefold Repetition

Evaluate (7/9) * (26/28) * (63/65) * ....... * [(k^3 - 1)/(k^3 + 1)] * .......

ralphmerridew · Daedalian Member

Product of first termsup to k==N is 2(N^2 + N + 1) / 3 (N^2 + N). (straightforward proof by induction)
Taking the limit as N->oo is 2/3.