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I am trying to get WolframAlpha to solve a recurrence and evaluate a result in one query.

For example: If

f[6] == 0, f[0] == 1 
f[i] == (1/2)*f[i+1] + (1/2)*f[i-1]

Then f[3] equals to .. ?

It gives me an analytical result for f, but does not evaluate f[3].

How would I get it to evaluate f[3] on this same query ?

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closed as off-topic by Sjoerd C. de Vries, Yves Klett, Mike Honeychurch, István Zachar, m_goldberg Oct 23 '13 at 10:29

  • The question does not concern the technical computing software Mathematica by Wolfram Research. Please see the help center to find out about the topics that can be asked here.
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Hello josinalvo, welcome to Mathematica.SE! Your question is about Wolfram Alpha, which is explicitly off-topic on this site. I won't close your question on this occasion, because @Tangshutao has provided a Mathematica answer that some people have upvoted. But please in future ask questions about the software Mathematica here, not about Wolfram Alpha. –  Verbeia Oct 23 '13 at 5:36
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This question appears to be off-topic because it is about Wolfram Alpha, which is officially off-topic here. –  Sjoerd C. de Vries Oct 23 '13 at 5:51
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1 Answer

You can use the RSolve command:

RSolve[{a[n] == 1/2 (a[n + 1] + a[n - 1]), a[0] == 1, a[6] == 0}, a[n], n]

{{a[n] -> (6 - n)/6}}

{{a[n] -> (6 - n)/6}} /. n -> 3

{{a[3] -> 1/2}}

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