Sec 11.3 Geometric Sequences and Series
... Sec 11.3 Geometric Sequences and Series Objectives: •To define geometric sequences and series. •To define infinite series. •To understand the formulas for sums of finite and infinite geometric series. ...
... Sec 11.3 Geometric Sequences and Series Objectives: •To define geometric sequences and series. •To define infinite series. •To understand the formulas for sums of finite and infinite geometric series. ...
Diophantine Representation of the Fibonacci Numbers
... MatijaseviS [ 8 ] , [9] showed that no such algorithm exists. He proved this by proving that every recursively enumerable set is Diophantine. The Fibonacci numbers were important in MatijaseviFs proof, because the sequence of Fibonacci numbers grows exponentially. Martin Davis, Julia Robinson and Hi ...
... MatijaseviS [ 8 ] , [9] showed that no such algorithm exists. He proved this by proving that every recursively enumerable set is Diophantine. The Fibonacci numbers were important in MatijaseviFs proof, because the sequence of Fibonacci numbers grows exponentially. Martin Davis, Julia Robinson and Hi ...
Chapter 2 Summary
... Determine the appropriate inequality symbols which will make each statement true (more than one symbol may apply). ...
... Determine the appropriate inequality symbols which will make each statement true (more than one symbol may apply). ...
On a conjecture of Chowla and Milnor
... Proof Let χ be a non-trivial quadratic character modulo q which is even. For such a character, we have L(k, χ) = ...
... Proof Let χ be a non-trivial quadratic character modulo q which is even. For such a character, we have L(k, χ) = ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.