Tagged Questions
0
votes
0answers
22 views
Is this equation on the right form?
Lets assume there is a list $l$, where its items are denoted as $[a_0,...,a_n]$ and where we only consider the first and last third without the elements in b/n and while doing it recursively until we ...
1
vote
1answer
58 views
Recurrence Equation with Polynomial Coefficients
As inspired by this question on the problem site Brilliant,
Let $F_n(a,b,c)=a(b-c)^n+b(c-a)^n+c(a-b)^n$
Is it possible to obtain $F_n$ in terms of $F_3, F_2$?
My attempt at a solution is as ...
2
votes
1answer
54 views
Recurrence relation help
The function $\psi_k(n)$ satisfies the recurrence relation:
$$\sum_{j=0}^k\binom{k}{j}(-1)^j\psi_j(n)\ln(n)^{k-j}=\psi_k(n)$$
Using this, is there a general way I can re-write
the function $
...
1
vote
6answers
93 views
limit of convergent series
What is the limit of $U_{n+1} = \dfrac{2U_n + 3}{U_n + 2}$ and $U_0 = 1$?
I need the detail, and another way than using the solution of $f(x)=x$, as $f(x) = \frac{2x+3}{x+2}$ because I can't show ...
2
votes
1answer
342 views
Recurrences that cannot be solved by the master theorem
I am given this problem as extra credit in my class:
Propose TWO example recurrences that CANNOT be solved by the Master Theorem.
Note that your examples must follow the shape that $T(n) = ...
6
votes
1answer
228 views
Proving or disproving $f(n)-f(n-1)\le n, \forall n \gt 1$, for a recursive function with floors.
The Olympiad-style question I was given was as follows:
A function $f:\mathbb{N}\to\mathbb{N}$ is defined by $f(1)=1$ and for $n>1$, by: ...
0
votes
1answer
408 views
Linear homogeneous recurrence relation with constant coefficients: How does one determine the solution set?
According to my textbook and this Wikipedia article, a recurrence relation of the form
$$ b_0 a_n + b_1 a_{n-1} + \cdots + b_k a_{n-k} = 0 $$
(EDIT: where $ b_0 \neq 0 $) has the following set of ...
3
votes
3answers
222 views
expansion of $\cos^k(\theta)$
Does any body know a expansion of :
$\cos^k(\theta)$ in function of $\cos$ and/or $\sin$ but without power?
For example : $\cos^2(\theta)=\frac{1}{2}(\cos(2\theta)+1)$, but i would want a ...
3
votes
2answers
740 views
Deriving formulas for recursive functions
If I had a recursive function (f(n) = f(n-1) + 2*f(n-2) for example), how would I derive a formula to solve this? For example, with the Fibonacci sequence, Binet's ...
