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Math Help - Show Function Satisfies Equation

  1. #1
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    Show Function Satisfies Equation

    1) Assuming that f(0) = 0, show that f(n) = n * (n+1) / 2 satisfies the equation:

    f(n) = n + f(0) + f(n-1)

    2) Show that g(n) = n log n, satisfies the equation:

    g(n) = n + 2g * (n/2)
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  2. #2
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    Well we are given f(n) and f(0) so lets start by plugging them in first.

    \displaystyle \frac{n(n+1)}{2}=n+0+\frac{(n-1)n}{2}=n+\frac{n(n-1)}{2}=\frac{2n+n(n-1)}{2}=.....

    You should be able to finish this and use the same methodology for number 2.

    As a side note, \displaystyle \frac{n(n+1)}{2}=\sum_{i=1}^{n}i
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  3. #3
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    I am not sure how to finish it, what are you doing each time and what fills the dots after the equals?
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  4. #4
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    I just plugged in the values to the equation. We were given f(n) and f(0) so I substitute those in to the equation f(n)=n+f(0)+f(n-1).

    For f(n-1), I plugged in n-1 for n in the f(n) equation. Thus, \displaystyle f(n-1)=\frac{(n-1)(n-1+1)}{2} and simplify. Now, we have all pieces to our f(n) equation. From here, your goal is to make the left hand side(LHS) look like the RHS.
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  5. #5
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    Please could you help me on part 2?

    What software did you use to create the math equations into images?
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  6. #6
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    Quote Originally Posted by NightFire91 View Post
    Please could you help me on part 2?

    What software did you use to create the math equations into images?
    I uised the latex feature of the website you type [tex] equation [tex] but the last math has to be
    /math in brackets.
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  7. #7
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    Well we know g(n)=n log(n)

    So..

    [Math]nlog(n)=n+2g\left(\frac{n}{2}\right)[/tex]

    What is g(n/2)=??
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