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... A rational number r is said to be divisible by a prime number p provided the numerator of r is divisible by p . Here it is assumed that all rational numbers are written in standard form. That is, the numerators and denominators are relatively prime integers and the denominators are positive. Certain ...
... A rational number r is said to be divisible by a prime number p provided the numerator of r is divisible by p . Here it is assumed that all rational numbers are written in standard form. That is, the numerators and denominators are relatively prime integers and the denominators are positive. Certain ...
Sequences and Series
... An arithmetic sequence is one where a constant value is added to each term to get the next term. example: {5, 7, 9, 11, …} A geometric sequence is one where a constant value is multiplied by each term to get the next term. example: {5, 10, 20, 40, …} EXAMPLE: Determine whether each of the following ...
... An arithmetic sequence is one where a constant value is added to each term to get the next term. example: {5, 7, 9, 11, …} A geometric sequence is one where a constant value is multiplied by each term to get the next term. example: {5, 10, 20, 40, …} EXAMPLE: Determine whether each of the following ...
Sequences and Series I. What do you do when you see sigma
... To find the nth term in a geometric sequence you may use the formula An = A1rn - 1 Where An is the nth term, A1 is the first term, r is the common ratio, and n is the position of the term. ...
... To find the nth term in a geometric sequence you may use the formula An = A1rn - 1 Where An is the nth term, A1 is the first term, r is the common ratio, and n is the position of the term. ...
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.