Prove that $$1+z+2z^2+3z^3+5z^4+8z^5+13z^6+...=\frac{1}{1-(z+z^2)}$$
The coefficients are Fibonacci numbers, i.e., the sequence $\left\{1,1,2,3,5,8,13,21,...\right\}$.
Socratic method, also known as maieutics, method of elenchus, elenctic method, or Socratic debate, is a form of cooperative argumentative dialogue between individuals, based on asking and answering questions to stimulate critical thinking and to draw out ideas and underlying presumptions. It is a dialectical method, often involving a discussion in which the defense of one point of view is questioned; one participant may lead another to contradict themselves in some way, thus weakening the defender's point. This method is named after the classical Greek philosopher Socrates and is introduced by...
This code-golfchallenge was inspired by this post. I'm looking for some feedback. Does this seem like a decent enough challenge? I'm still thinking up rules and a title - suggestions are very much welcome.
Challenge
Take an array of non-negative integers.
[1,4,7,2,8,4,6,8]
Separate the even ...
The Basel problem is a problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1644 and solved by Leonhard Euler in 1734 and read on 5 December 1735 in The Saint Petersburg Academy of Sciences (Russian: Петербургская Академия наук). Since the problem had withstood the attacks of the leading mathematicians of the day, Euler's solution brought him immediate fame when he was twenty-eight. Euler generalised the problem considerably, and his ideas were taken up years later by Bernhard Riemann in his seminal 1859 paper On the Number of Primes Less Than a Given...
Hot Potato code-challenge
For this code-golf challenge you are to play hot potato with two friends (let's name him Dennis and Martin for no apparent reason). The goal here is to see if you can beat both Dennis and Martin.
Rules:
One player starts with the potato
The player holding the potat...
Output every string
code-golf
Your task here is simple. Write a program, in as few bytes as possible, which prints every single possible string. Your program should, given infinite memory, never terminate, however for any given string there should be a finite time to be generated. (that is, a a...
Inspired by this challenge
Given an integer, output the minimum sized container it can fit in out of
bit: 1
nybble: 4
byte: 8
short: 16
int: 32
long: 64
You will not be asked to classify any numbers that are higher than 2**64-1.
Testcases:
0 -> 1
1 -> 1
2 -> 4
15 -> 4
16 -> 8
123 -> 8
260 ->...
0
You're sick of other players smugly announcing "BINGO" and walking triumphantly past you to claim their prize. This time it will be different. You bribed the caller to give you the BINGO calls ahead of time, in the order they will be called. Now you just need to create a BINGO board that will win...
0
Compress a Tic-Tac-Toe board code-challenge compression
Preface
Let us think of a Tic-Tac-Toe board as a 0-indexed matrix:
image coming soon!
With each square assigned to a coordinate, we can represent any Tic-Tac-Toe game as a list of moves:
X: Take (1, 0)
O: Take (1, 1)
X: Take (2, 0)
O...
