Riddles/Math/Logic

This is a discussion on Riddles/Math/Logic within the A Brief History of Cprogramming.com forums, part of the Community Boards category; Originally posted by Nick I noticed that derivative of 1 + t + t^2 + t^3 + ... + t^n ...

  1. #31
    Registered User rahaydenuk's Avatar
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    Originally posted by Nick
    I noticed that derivative
    of 1 + t + t^2 + t^3 + ... + t^n
    is the 0 + 1 + 2t + 3t^2 +... + nt^(n-1)
    I'm sure you could give a prove or solve it some how
    using this?
    Exactly! Well done.

    If you sum the first series, using the standard geometric series result, you can then differentiate that result to get the sum of the second series, which is the same answer as you got.

    Like this:

    Summing first series (using standard geometric series result):

    1 + t + t^2 + ... + t^n = (1 - t^(n+1))/(1 - t)

    d(1 + t + t^2 + ... + t^n)/dt = 1 + 2t + 3t^2 + ... + nt^(n - 1)

    Which implies that:

    1 + 2t + 3t^2 + ... + nt^(n - 1) = d((1 - t^(n+1))/(1 - t))/dt
    = (1 - t^n + nt^(n + 1) - nt^n)/((1 - t)^2)

    I think that's quite a nice little solution...
    Richard Hayden. (rahaydenuk@yahoo.co.uk)
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  2. #32
    Blank
    Join Date
    Aug 2001
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    If you havn't got it already check out
    concrete mathematic --- A foundation for computer science.
    Lots of neat problems, most of them are solved in the back
    of book.

    I'm trying to read this book in my spare time, but I have
    lots of course work so I havn't gotten too far. It's tough
    to read.

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