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    Several proofs by induction

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    Show by induction that:

    a) Sum(n^2/[(2n-1)*(2n+1)],n=1..) = n(n+1)/[2*(2n+1)]

    b) Sum( r/(r-1)!, r=1..n) = 1-1/(n+1)!

    c) n^3+3n^2-10n is divisible by 3

    d) 4^(2n+1) + 3^(n+2) is divisible by 13

    See attached file for full problem description.

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    Solution Preview

    Please see the attached file.
    Just for the record:
    I had to change problem b.
    It should read
    Sum(r/(r+1)!) rather than Sum(r/(r-1)!). ...

    Solution Summary

    The solution demonstrates the use of induction in proving mathematical identities.