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2. Wheat and chessboard problem - Wikipedia

   en.wikipedia.org/wiki/Wheat_and_chessboard_problem

   When expressed as exponents, the geometric series is: 2 0 + 2 1 + 2 2 + 2 3 + ... and so forth, up to 2 63. The base of each exponentiation, "2", expresses the doubling at each square, while the exponents represent the position of each square (0 for the first square, 1 for the second, and so on.). The number of grains is the 64th Mersenne number.

3. How to Solve It - Wikipedia

   en.wikipedia.org/wiki/How_to_Solve_It

   First, you have to understand the problem. [2] After understanding, make a plan. [3] Carry out the plan. [4] Look back on your work. [5] How could it be better? If this technique fails, Pólya advises: [6] "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?"

4. Exponentiation - Wikipedia

   en.wikipedia.org/wiki/Exponentiation

   This definition of exponentiation with negative exponents is the only one that allows extending the identity + = to negative exponents (consider the case =). The same definition applies to invertible elements in a multiplicative monoid , that is, an algebraic structure , with an associative multiplication and a multiplicative identity denoted 1 ...

5. 10 Hard Math Problems That Even the Smartest People in the ...

   www.aol.com/10-hard-math-problems-even-150000090...

   Here’s another problem that’s very easy to write, but hard to solve. All you need to recall is the definition of rational numbers. Rational numbers can be written in the form p/q, where p and ...

6. Multinomial theorem - Wikipedia

   en.wikipedia.org/wiki/Multinomial_theorem

   The third power of the trinomial a + b + c is given by (+ +) = + + + + + + + + +. This can be computed by hand using the distributive property of multiplication over addition and combining like terms, but it can also be done (perhaps more easily) with the multinomial theorem.

7. Equation solving - Wikipedia

   en.wikipedia.org/wiki/Equation_solving

   When the task is to find the solution that is the best under some criterion, this is an optimization problem. Solving an optimization problem is generally not referred to as "equation solving", as, generally, solving methods start from a particular solution for finding a better solution, and repeating the process until finding eventually the ...