# Tagged Questions

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### Discrete math and recursion problem.

I was recently reading up examples on recursion and how it relates to induction and there's this question I am not sure about. Q: Let $$b_1=3$$ $$b_n=n(n+2)$$ From that question I wanted to do the ...
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### Check these recursive definitions for me?

Looking for Give a recursive definition of A) the set of odd positive integers B) the set of positive integer powers of 3 C) the set of polynomials with integer coefficients I have a. Basis: ...
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### Define this recursively : $f(n) = 3n - 4$

Define this recursively : $f(n) = 3n - 4$ I thought this is how you recursively define a function? $f^{-1}(n): y = 3n-4$ $y+4 = 3n$ $f^{-1}(n) = (y+4/3)$ But the answer is $f(n) = f(n-1) + B$ ...
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### How do you use induction on a recursive sequence using different variables?

I've been working on some recursive sequences for my Discrete class. I've understood most of them, but I've come to a new question which I'm confused about. A sequence $C_{0}$, $C_{1}$, $C_{2}$ is ...
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### Figuring out the steps in a Recursive Function

I have the following recursive function: $f(0) = 7$ $f(n+1) = f(n) + 6n + 1$ for all integers $n => 0$ I know the answer is $f(n) = 3n^2 + 2n + 7$ I would like to know the steps to get to this ...
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### Mathematical Induction Recursion

Consider the recursion given by $f(n) = 2f(n−1)− f(n−2)+6$ for $n ≥ 2$ with $f (0) = 2$ and $f (1) = 4.$ Use mathematical induction to prove that $f (n) = 3n^2 −n+2$ for all integers $n ≥ 0.$
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### Proving a recurrence relation for strings of characters containing an even number of $a$'s

We consider strings of $n$ characters, each character being $a$, $b$, $c$, or $d$, that contain an even number of $a$'s. (Recall that $0$ is even.) Let $E_n$ be the number of such strings. ...
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### Creating Recurrence

If I have an integer $n \geq1$, and I had to draw $n$ straight lines, so that no two of them are parallel as well as no three of them intersect in one single point. These lines divide the plane into ...
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### Recursion definition

Give a recursive defintion of the following set: $\{ 5^m 7^n \mid m, n \in N \}$ I don't have the slightest idea how to approach this question, id be really grateful if someone could provide me with ...
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### Difficult recursion problem

A student can do the things bellow: a. Do his homework in 2 days b. Write a poem in 2 days c. Go on a trip for 2 days d. Study for exams for 1 day e. Play pc games for 1 day A schedule of n days ...
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### Discrete Mathematics - Recursion

Given the following question by my professor: Recursively define the set of natural numbers divisible by 3. My answer: ...
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### Number of ways to arrange different poker chips. (Recursion)

Assume there are poker chips in four different colors and one of the colors is blue. In how many ways can n amount of chips be piled on top of each other without two blue ones being next to one ...
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### factoring cubic polynomail equation using Krammer's rule.

1) I have question about factoring cubic polynomials. In my note it says "Any polynomial equation with positive powers whose coefficients add to 0 will have a root of 1. Another, if sum of the ...
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### Recursively defines function

Find $f(2),f(3),f(4)$, and $f(5)$ if $f$ is defined recursively by $f(0)=-1$, $f(1)=2$, and for $n=1,2,\ldots$ $$f(n+1)= 3f(n)^2 - 4f(n-1)^2$$
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### Recursive Formula

I have found a question in my book and I have solve it, but I am not sure about the answer. The question goes like this: Find a recursive formula that will give the number of ways to order $N$ ice ...
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### Golf Player Balls

A golf player has $K$ balls of the same type and $N$ balls of different types. I. In how many ways can we paint the balls such that each ball will be painted only once (the order of balls in the bag ...
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### Basic Recursion Exercise

Find a recursive formula to divide N people in to couples and singles. The answer: $$A_n = A_{n-1} + A_{n - 2}(n - 1)$$ Some one can explain the answer , why do we need to multiply by n-1?
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### Basic Discrete Mathematics Question

I was preparing my self before an exam and I found this question: For each of the following equations, find a positive integer $n$ that satisfies the equation. The notation $p(n,r)$ stands for ...
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### Can't understand a recursive definition of concatenation of two strings

I'm reading Rosen's Discrete Mathematics and its applications(6ed), but I can't understand a recursive definition about concatenation of two strings: Two strings can be combined via the operation ...
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### Recursively Defined Entities

So I am having some trouble understanding how one is to come up with the recursive definition to the following problem... We are given a rectangle of width $2$ and length $n$. Suppose we have ...
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### Give a recursive definition with initial condition…how did they get the answer?

The function $f (n) = 5n + 2, n = 1, 2, 3, \ldots$ Im sure its a simple problem, but im really confused...how did they get the answer ? could someone explain $f (n) = f (n - 1) + 5, f (1) = 7$ ...
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### Explanation of the recursion for number of surjections

I have a question about the recursion of the number of surjections from $\{1,\ldots,n\}$ to $\{1,\ldots,k\}$: $$\mathrm{Sur}(n,k) = k \cdot \mathrm{Sur}(n-1,k-1) + k \cdot \mathrm{Sur}(n-1,k).$$ My ...
Let $A(k)$ be the number of distinct binary strings of length $2k+1,$ for which the number of $1$s surpasses the number of $0$s for the first time at digit number $2k +1$, i.e., in the final digit in ...