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Product of Sum and Product (Posted on 2012-06-21) Difficulty: 3 of 5


Let {an} be a sequence of real numbers defined by

    a0 ∉ {0,1},
    a1 = 1 - a0, and
    an+1 = 1 - an(1 - an) for all n ≥ 1.

Let Pn and Sn be defined by

    Pn = a0a1a2 ··· an and

    Sn = 1/a0 + 1/a1 + 1/a2 + ··· + 1/an

for all n ≥ 0.

Prove the following

    PnSn = 1 for all n ≥ 0.

See The Solution Submitted by Bractals    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolutionJohn Dounis2012-06-24 09:49:59
SolutionSolutionJohn Dounis2012-06-24 09:43:51
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