2
votes
1answer
22 views

How would I go about converting $U(n)= 4^n+U(n-1)$ into an explicit form? [closed]

I have the recursive function $U(n)= 4^n+U(n-1)$, and I'd like to convert it into an explicit form. If you could also walk me through the process that would be great. Thanks!
0
votes
1answer
24 views

Recursively calculate grand total

Starting January, I have a value of 2.5. Each month I add 2.5. I believe that I = Prt will tell me the final value in December, but I need the running total. Ex: ...
1
vote
3answers
148 views

Recurrence relations (Big-O notation)

Say I'm given a recursive function such as: function(n) { if (n <= 1) return; int i; for(i = 0; i < n; i++) { function(0.8n) } } ...
4
votes
3answers
66 views

Recursion, multiplication and exponential

The set $F_{n}$ of primitive recursive function symbols of arty $n$ can be defined inductively as \begin{array}[lr] & Z, \text{Succ} \in F_{1} & \\ \pi_{j}^{n} \in F_{n} \quad \text{for each} ...
0
votes
1answer
25 views

Defining a recursive function $f$ on $\{a, b\}$*

I would need some help on how I can define a recursive function $f$ on $\{a, b\}$* Define a recursive function $f$ on $\{a, b\}$* which replaces any $a$ with $b$ and vice versa, for example, ...
0
votes
2answers
58 views

I need some help on solving a recursive function question

I'm working on a recursive function task which i'm a bit stuck at. I've tried to google it on how I can solve this task, but with no luck Here is the task: Provide a recursive function $r$ on ...
0
votes
1answer
73 views

How can I solve this recursion function task?

I really need help on this task. Im stuck at it and I really would appreciate your help here. Give a recursive function $r$ on $A$ that reverses a string. For instance, $r(logikk) = kkigol$ and ...
0
votes
2answers
73 views

How could I describe a function whose domain is x>=1 for integers, starts at 3 f(1)=3, then multiplied by 2 f(2)=6, then by 3 f(3)=18, repeat

$$f(1)=3 \quad f(2)=6\quad f(3)=18\quad f(4)=36 \quad f(5)=108$$ How can I define this function? The function is recursive and multiplies by 2 then 3 alternatively. I know I could solve this in ...
2
votes
1answer
53 views

help deriving a closed formula for this “magic function”

I'm having trouble coming up with a closed formula for $n$ from the sequence of numbers generated by this function: The following mystery function $M : N \times N \rightarrow N $ is defined by: $$ ...
1
vote
3answers
59 views

Recursively Defined Functions

I am taking a summer class in discrete math and have done very well up till now. I am nervous because I have reviewed the lecture slides and practice problems but I still don't really understand what ...
0
votes
2answers
87 views

Recursive function into non-recursive

I have to express $a_n$ in terms of $n$. How do I convert this recursive function into a non-recursive one? Is there any methodology to follow in order to do the same with any recursively defined ...
5
votes
2answers
182 views

Repertoire method for solving recursions

I am trying to solve this four parameter recurrence from exercise 1.16 in Concrete Mathematics: $g(1) = \alpha;$ $g(2n+j) = 3g(n) + γn + β_j$ : j = 0,1 and n >= 1 I have assumed the closed form to ...
1
vote
1answer
76 views

Recursive function

For a sequence $a$, $a_1=2$, $$a_n=\frac{n-1}{a_{n-1}}+n-1$$Express $a_n$ in terms of $n$. I tried keep expanding, got many level of fraction until $n=1$, but I still can't see the pattern. ...
1
vote
5answers
237 views

Any fastest algorithm for $f(n) = f(n-1) \cdot f(n-2)$ where $3 \leq n \leq 1000000$

Any fastest algorithm for $$ f(n) = f(n-1)\cdot f(n-2)\quad\text{ where }\quad f(1) = 1,\quad f(2) = 2 $$ for $3 \leq n \leq 1000000 $.
0
votes
1answer
51 views

Algorithms and generalisation of functions

I admit I'm little bit poor in functions in mathematics. But I'm in real urge to get this riddle out. How to express $$x(n)=x(n-1)+x(n-2)+1,$$ where $n>1$ and $x(0)=0$ and $x(1)=1$, in terms of ...
3
votes
1answer
183 views

Nesting functions to understand nesting series

So I am working on a problem that involves an expression that has a "nested" sigma notation. Maybe "nested" isn't the correct word, because you start with an input (of your choosing) and the output ...