perplexus.info :: Sequences : Initial Term Identification

Initial Term Identification (Posted on 2015-07-21)

A sequence {X₀, X₁, X₂, ...., X_n} is given by:
X_n(1 - X_n-1) = X_n-1

Find X₀, given that: X₂₀₁₅ = 2015

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Working from the other direction

| Comment 2 of 3 |

x(1) = x(0)/(1 - x(0))

x(2) = x(1)/(1 - x(1)) = x(0)/(1 - 2*x(0))

x(3) = x(0)/(1 - 3*x(0))

x(2015) = x(0)/(1 - 2015*x(0)) = 2015

x(0) = 2015/(2015^2 + 1) = 2015/4060226

Posted by xdog on 2015-07-21 19:57:58

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