1. S

    Idea for Recursive Algorithm

    I have a question and I knew you cannot give a complete solution and I need some tips. I should solve this problem with the recursion algorithm. For the last row: The first and second numbers add together then second and third numbers add together and finally third and fourth number add...
  2. L

    proof of recursive identity

    How can this be handled?
  3. B

    Mathematical Induction Recursive Function Help!

    T(n) = \begin{cases} 2, \quad n=2 \\ 2T(n/2) + n, \quad n=2^k \quad k>1 \end{cases} Prove (If n is a power of 2) using mathematical induction that: T(n) = n\log_2(n) I tried it but I can't solve it, probably because I don't know how to use the information that n is a power of two. This is...
  4. C

    Find a recursive formula for the number of combinations

    I have some question integrating between combinatorics and recursive formulas. Generally, I have some difficulty with the concept of recursion, as well as with the recursion in programming unfortunately. I have some question to solve, and maybe you can guide me: Find a recursive...
  5. C

    Recursive definition and induction

    Hey. The series $a_n$ is defined by a recursive formula $a_n = a_{n-1} + a_{n-3}$ and its base case is $a_1 = 1 \ a_2 = 2 \ a_3 = 3$. Prove that every natural number can be written as a sum (of one or more) of different elements of the series $a_n$. Now, I know that is correct intuitively...
  6. A

    Regression tree, recursive partition.

    Hello, I am really struggling with some basic things related to regression tree. Mainly I do not understand how I am suppose to calculate square error and form the recursive partition. Here is the set-up: I have a dataset $\{((1,1),9),((1,2),-4),((1,3),2),((2,2),4),((2,3),2)\}$ and I need...
  7. S

    Recursive sequence

    I would just like someone to check this and tell me if I got this correctly. So I got a recursive sequence first term : aˇ1 = 21 aˇ(n+1) = (aˇn + 6)^(1/3) --> cubic root so I have to check if i't's convergent which should be, that it is either : 1. monotonic, decreasing and has...
  8. B

    Recursive equation

    Hello! I wasn't really sure where to post this, but I figured I put it here since recursive equations are fairly similar to differential eqs. Anyway, I went through an earlier exam from my school and stumbled upon this equation: s_{n+1}-s_n = n^2+2n+1. The answer is...
  9. J

    Please helps!

    3, 5 1/2, 10 1/2, 20 1/2.. write the recursive and explict rule write the difference
  10. F

    limit of a recursive sequence

    let (a_n) be a sequence such that: a_(n+2)=1/3*a_(n+1)+2/3*a_n what is the limit of (a_n)? [the fact it converges has already been proved earlier in the question and we are not given a(1) and a(2)]
  11. L

    recursive integration,integration done, how to get formula

    Hi there :). I need to integrate function dx/sin^n (x). I did the integration part, i believe it is right. In=- In-2 -2/(n*sin^n(x) I am sorry for formula written like this , I am learning coding so I hope I'll soon be able to write it better. So now i thing the condition should be n>=2...
  12. K

    recursive equations

    R= { (1,1), (1,2), (1,4), (2,2), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (4,4), (5,1), (5,3) } a- Show the MR matrix . b- S= { (1,2), (1,3), (1,4), (2,2), (2,3), (2,5), (3,1), (3,2), (3,5), (4,2), (4,4), (5,1), (5,2) } MS o R = ?
  13. D

    Fundamental operations and recursive operations

    Hi folks, I'm trying to create a mathematical formula evolution program, I represent formulae as node trees which acts as the genome, which in (my) theory can express any formula that can exist by using numbers as the leaf nodes, and the four fundamental math operations namely; Add, Subtract...
  14. S

    Ackermann function and primitive recursive functions

    Hello, I see everywhere written that Ackermann function is not primitive recursive function, because it grows faster than primitive recursive functions. I can't get the idea what was meant by saying grows faster than primitive. So, can anyone explain step by step what it means that Ackermann...
  15. S

    minimization operator for partial recursive functions

    Hello, can someone give me a few examples of how minimization operator works for partial recursive functions? So far I have read: Recursive Functions (Stanford Encyclopedia of Philosophy) μ operator - Wikipedia, the free encyclopedia μ-recursive function - Wikipedia, the free...
  16. B

    Recursive integral function

    Hi, I was lastly intrigued by the possibility of graphing a recursive integral function with formula: f(x)=\int_{0}^{x}f(x-1)+x\, dx I started with evaluating a limit with n approaching infinity, where n is the number of recursive iterations, but I am not so advanced to be able to calculate...
  17. S

    Formulating a recursive function

    I am trying to create a formula for something that is probably really easy for some. If some one can help me out that would be great! I need to write a general formula for: the function depends on the turn. start with a base number, n. Multiply the base number by 3, divide it by two and add...
  18. B

    recursive formula

    write down a recursive formula for this sequence 1; 5 ; 13 ; 29 ;69 how do I approach recursive sequences?
  19. B

    Brainwaves as recursive signal processing

    Something I wrote titled "Lets try Test Driven Development for Vision AI", but its really about narrowing down a kind of intelligent signal processing more than any specific way to build it. Call it software only if its calculus derivative is undefined. There is a "bill clinton neuron" in many...
  20. S

    About an erroneous recursive definition

    Hi, I'm reading Introduction to set theory of Monk, and on page 87 in the paragraph of recursive definitions, it starts with a wrong proof about the existence and uniqueness of such a recursive function. The example function is that of addition. The argument is by induction: m+n is defined for...