# recursive

1. ### Recursive Question - Discrete Maths

Let b0, b1, b2, . . . be the sequence defined recursively as b0 = 0, bk = k − bk−1 for each integer k ≥ 1. (a) Write out the first 8 terms of this sequence, and use that information to guess an explicitformula for this sequence. (b) Prove that your guess of an explicit formula is correct. I...
2. ### MATLAB Question - Entering recursive definitions

Hi Thanks to all that have helped me so far. I have a question regarding Matlab if anyone can help: My question asks me to write a recursive definition from a word question: the recursive formula is: w(n) = (8000 - (250n/(n+1)) x 0.02 At this point I am a little confused as to whether...
3. ### Recursive and General Formula Finding - not done maths for 20 years

Hi All I am new to the forum and though you may be able to help. I want to check I have the following questions correct before going any further: (a) Find, showing all working, a formula for the n-th term tn of the sequence (tn) defined byt1 = 6; t(n) = −3t(n−1)/2, n ≥ 2. (b) Find, showing...
4. ### Recursive sequence

$\text{I don't know how to find the general formula for the sequence: }\\ (x_n):x_{n+1}=\frac{ax_n+b}{cx_n+d},\text{ with } x_1,a,b,c,d\in\mathbb{R} \text{ given.}\\ \text{I know there are some formulas but a couldn't find them. Please help!}$
5. ### The recursive formula for the series.

See the picture a) Since $a_{1}=4/3$ so there must be $a_{n}=4/3$ for all $n\geq 1$. The statement is clearly true for $n=1$. Assume that the statement is true for $n=m$. Since $a_{m+1}=2-(1/2)a_{m}=2-(1/2)a_{n}=a_{n}$, so the statement is also true for $n=m+1$. We have shown that it is...
6. ### Explicit (General) formula for recursive definition.

I am given an = 3an-1 + 4^n, n = 1,2,3,... and a0 = 1. First four terms: a1 = 3*1 + 4^1 = 3+4 = 7 a2 = 3*7 + 4^2 = 21 + 16 = 37 a3 = 3*37 + 4^3 = 111 + 64 = 175 a4 = 3*175 + 4^4 = 525 + 256 = 781 Now I can't see any pattern going on, such that I could write it in form of a sequence formula.
7. ### Explicit Formula to Recursive sequence

I need to turn Un=81(1/3)^n-1 into a recursive sequence. If you cold explain why each part goes where is does that would be wonderful too.
8. ### How can I solve this recursive relation?

How can I solve this recurrence relation? \\f(n, m) =\begin{cases}0, & \text{if }n,m < 0\\1, & \text{if }n,m = 0\\\sum_{i = 0}^{k = max(n, m)}([f(n - i, m - [k - i]) + c]\binom{k}{i}) - c(2^{k - 1} + 1), & \text{otherwise}\end{cases}
9. ### List the elements of S produced by the first five applications of the recursive defin

Let S be the subset of the set of ordered pairs of integers defined recursively by Basis step: (0, 0) ∈ S. Recursive step: If (a, b) ∈ S, then (a + 2, b + 3) ∈ S and (a + 3, b + 2) ∈ S. a) List the elements of S produced by the first five applications of the recursive definition. How do...
10. ### Recursive sequence limit challenge

Hi, I saw this problem in Coursera's Calculus II by the Ohio State University: Most of us are familiar with the Fibonacci Sequence With\quad F_{ 0 }={ F }_{ 1 }=1\\ \\ { F }_{ n }={ F }_{ n-1 }+{ F }_{ n-2 }\\ \\ \left\{ 1,1,2,3,5,8,13,21,...{ F }_{ n } \right\} Now we can build { G }_{ n...
11. ### [HARDCORE] first order recursive sequence problem.

Here is a problem I need to investigate from my 300 level calculus course. But I'm a stats student!!!! I've forgot most of hardcore calculus from first year courses. Especially sequence convergence stuff. Please help me with this. Define the following first-order recursion that depends on the...
12. ### Variation on Recursive Bayesian Estimation

Hi, I'm doing a research on a variation of Recursive Bayesian Estimation- it's a Bayesian estimation with a 'time smoothing' term: { \hat { P } }_{ k+1 }(x)\quad =\quad \eta \cfrac { { \hat { P } }_{ k }(x)p({ z }_{ k+1 }|x) }{ \int _{ -\infty }^{ \infty }{ { \hat { P } }_{ k }(x)p({ z }_{...
13. ### Recursive Derangement Formula proof

I'm stuck on the proof in the title. Consider a derangement on {1,2,...,n} Let Xk: set of derangements with the last element k Yk: set of derangements in Xk with the k-th element n Zk: set of derangements in Xk with the k-th element not n Then, (i) if entries n and k are deleted in...
14. ### Integration - Recursive Formulae

I did Integration by Parts and ended up with: I_n = e - nI_{n-1} Not sure where to head from here? Thanks.
15. ### system of recursive relations

Hi, everyone ! i want to know how to solve system of recursive relations. exactly, a_n = a_(n-1)^2 +b_(n-1)*c_(n-1) b_n = [a_(n-1) +d_(n-1)]*b_(n-1) c_n = [a_(n-1) +d_(n-1)]*c_(n-1) d_n = b_(n-1)*c_(n-1) + d_(n-1)^2 a_0, b_0, c_0, d_0 are give. What are a_n, b_n , c_n, d_n ? ( and what is...
16. ### Solving Recursive Equations - Domain Transformation

Hi all, So I've solved a recursive equation so far and I'm about to prove that it is correct through induction. However, before I get into that... here's what I have: I have 2 questions: (1) Why, at the end of the telescoping, does S(k) - 1 = k? How am I supposed to know what the final...
17. ### Writing a recursive definition for Sn

Find a formula for tn, the nth term of the series. Then give a recursive definition for Sn, the sum of n terms of the series. 1) 8+12+18+27+.... 2) 50+47+44+41+.... I know how to find the tn tn = tn-1 * (3/2) tn = 53-3n My teacher gave us the answers 1. Sn = Sn-1 + 8(3/2)^(n-1) 2. Sn =...
18. ### Recursive Algorithms - who is right? Lecturer or lab demonstrator?????

Hi everyone, I'm really stuck on the following two questions. In essence, our lecturer went through these examples in class and a week later, the exact same questions were put to our lab demonstrator from a student who failed to grasp the original lecture. The problem? the demonstrator's...
19. ### Finding the recursive definition for an integer sequence

I'm not sure I fully understand how to do a recursive definition for an integer sequence containing an exponent. a_n = 4^n + 12; \forall n \geq 0 I can figure out that: 4^0 + 12 = 13 4^1 + 12 = 16 4^2 + 12 = 28 4^3 + 12 = 76 4^4 + 12 = 268 which equates to (mutiples of 4) x 12...but I'm not...
20. ### Induction proof to prove recursive formula is equal to explicit formula

I'm really stuck on these, any help is appreciated. In each of the following a sequence is defined recursively. Guess an explicit formula for the sequence, then use mathematical induction to prove the correctness of your formula. Sorry I had some font sizing issues. If you can just explain the...