Recent content by JimmyK

If I have a recurrence equation of the following form: $$T(n) = T(km) = a, m = 1$$ $$T(n) = T(km) = T(k) + T(k(m-1)) + cn, m > 1$$ Where a is simply a constant, and k is an integer constant > 0. Now I begin substituting to find the pattern: $$T(k) = a$$ $$T(2k) = a + [a] + c2k$$ $$T(2k) = 2a...

So it seems like this is a Linear-Geometric Series. By applying the formula and if the lower bound was 1 instead of 2, I believe its closed form would be: $$\frac{-(n+1)(\frac{1}{x})^{n+1}+n(\frac{1}{x})^{n+2}+x}{(x-1)^{2}}$$ I wanted to make sure I'm taking the correct approach before...

Ah, I see that now. Thank you. So now I understand the common ratio in each distinct set is 1/x so I'm now working on trying to get the proper equation. :)

Thank you so much. I understand a bit more now, I guess I'm still a bit confused about $$\sum\limits_{i=2}^n \frac{i}{x^i}=2(\frac{1}{x^2}+\frac{1}{x^3}+\frac{ 1}{x^4}+\frac{1}{x^5}+...+\frac{1}{x^n})+(\frac{1}{x^3}+\frac{1}{x^4}+\frac{1}{x^5}+...+...

Thank you for expanding out the first few terms. I am try to find a general formula for it instead of using the summation notation.

I have the following summation and I'm attempting to remove the summation notation. It appears to be the sum of a geometric series but I'm having a great deal of trouble with it. X is an unknown constant. $$\sum\limits_{i=2}^n (n - (n-i))x^{n-i}$$ Thanks.

In class, we're learning about recursive functions. One example given was figuring out 1 + 2 + 3+ 4 + 5 + 6 + 7 + 8 + 9 + 10. My professor stated to address this, we start with 10 in the function and decrement for the next recursive call, so 10 + f(9). He said going the other way would be...