# Thread: Show Function Satisfies Equation

1. ## 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)

2. 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, $\displaystyle \frac{n(n+1)}{2}=\sum_{i=1}^{n}i$

3. I am not sure how to finish it, what are you doing each time and what fills the dots after the equals?

4. 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.

5. Please could you help me on part 2?

What software did you use to create the math equations into images?

6. Originally Posted by NightFire91
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 $$equation [tex] but the last math has to be /math in brackets. 7. Well we know $g(n)=n log(n)$ So.. [tex]nlog(n)=n+2g\left(\frac{n}{2}\right)$$

What is g(n/2)=??