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A Place for Beautiful Mathematics. Martin Erickson (1963 - 2013). What Is The Sum? Using a multiplication trick, generalizing a well-known formula. Some Two-Player Achievement Games. Adventures with Generating Functions V. Adventures with Generating Functions IV. Adventures with Generating Functions III. Adventures with Generating Functions II. How to make a million dollars. Adventures with Generating Functions I. Introducing a series on a useful tool, finding a sum involving Fibonacci numbers.

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Mathacadabra | mathacadabra.com Reviews

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A Place for Beautiful Mathematics. Martin Erickson (1963 - 2013). What Is The Sum? Using a multiplication trick, generalizing a well-known formula. Some Two-Player Achievement Games. Adventures with Generating Functions V. Adventures with Generating Functions IV. Adventures with Generating Functions III. Adventures with Generating Functions II. How to make a million dollars. Adventures with Generating Functions I. Introducing a series on a useful tool, finding a sum involving Fibonacci numbers.

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1 quick problems

2 algebra

3 arithmetic

4 number theory

5 advanced problems

6 combinatorics

7 geometry

8 discussions

9 probability

10 open problems

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quick problems,algebra,arithmetic,number theory,advanced problems,combinatorics,geometry,discussions,probability,open problems,games,guidelines for authors,recent items,level,date,three challenges,rook meanders,rook paths,integer triangles,order matters

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Mathacadabra | mathacadabra.com Reviews

https://mathacadabra.com

A Place for Beautiful Mathematics. Martin Erickson (1963 - 2013). What Is The Sum? Using a multiplication trick, generalizing a well-known formula. Some Two-Player Achievement Games. Adventures with Generating Functions V. Adventures with Generating Functions IV. Adventures with Generating Functions III. Adventures with Generating Functions II. How to make a million dollars. Adventures with Generating Functions I. Introducing a series on a useful tool, finding a sum involving Fibonacci numbers.

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mathacadabra.com

1

Mathacadabra

http://www.mathacadabra.com//Items2013/OrderedChangeForADollar.aspx

Note: this page uses MathJax for formatting, so may take a few seconds to load. Ordered Change For A Dollar. How many ways can you make change for a dollar if the order of the coins is important? Suppose that the available coins are pennies, nickels, dimes, quarters, and fifty-cent pieces. For example, two different ways to make change for a dollar are [ 5 25 25 25 10 10 quad mbox{and} quad 10 25 25 25 10 5. ]. What if we ask the same question, but where the order of the units does not matter?

2

Mathacadabra

http://www.mathacadabra.com//Items2013/GeneratingFunctionAdventuresII.aspx

Note: this page uses MathJax for formatting, so may take a few seconds to load. Adventures with Generating Functions II. Note: This is the second article of a planned 5-part series. The first article: Adventures with Generating Functions I: An Infinite Sum. Second Adventure: How Many Ways Are There to Make a Million Dollars? George Pólya showed how to solve this problem in his book How to Solve It. We can also solve the problem using generating functions. A computer algebra system tells us that the coeff...

3

Mathacadabra

http://www.mathacadabra.com//Items2013/DecimalChallenge.aspx

Note: this page uses MathJax for formatting, so may take a few seconds to load. If $( sqrt{2} sqrt{3}) {1000}$ is written in decimal notation, say, $a ka {k-1} ldots a 0.b 1b 2 ldots$, what are $a 0$ and $b 1$? From the definition of the sequences, [ ( sqrt{2}- sqrt{3}) {2n}=x n-y n sqrt{6}, ] and hence [ ( sqrt{2} sqrt{3}) {2n} ( sqrt{2}- sqrt{3}) {2n}=2x {n}. ]. Since $ sqrt{2}- sqrt{3}.

4

Mathacadabra

http://www.mathacadabra.com//Items2013/AgeOfDiophantus.aspx

Note: this page uses MathJax for formatting, so may take a few seconds to load. The Age of Diophantus. Diophantus of Alexandria (c. 210 - c 290 CE) discovered methods for finding integer or rational solutions to certain types of algebraic equations. A riddle from a work published around 500 purports to express the number of years that Diophantus lived (it isn't known whether the facts in the riddle are accurate):.

5

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http://www.mathacadabra.com//Items2013/SumOfReciprocals.aspx

Note: this page uses MathJax for formatting, so may take a few seconds to load. A Sum of Reciprocals. The $n$th triangular number. What is the sum of the reciprocals of all the triangular numbers, [ frac{1}{1} frac{1}{3} frac{1}{6} frac{1}{10} frac{1}{15} frac{1}{21} cdots ,? The trick is to write the reciprocal of a triangular number as a difference of fractions: [ frac{2}{n(n 1)}= frac{2}{n}- frac{2}{n 1}. ] Thus, the sum of the reciprocals of the triangular numbers is a telescoping series. Begin{align...

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mathacadabra.com

Mathacadabra

A Place for Beautiful Mathematics. Martin Erickson (1963 - 2013). What Is The Sum? Using a multiplication trick, generalizing a well-known formula. Some Two-Player Achievement Games. Adventures with Generating Functions V. Adventures with Generating Functions IV. Adventures with Generating Functions III. Adventures with Generating Functions II. How to make a million dollars. Adventures with Generating Functions I. Introducing a series on a useful tool, finding a sum involving Fibonacci numbers.

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