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  2. Carry (arithmetic) - Wikipedia

    en.wikipedia.org/wiki/Carry_(arithmetic)

    Some innovative machines use continuous transmission: adding 1 to any digit, advances the next one by 1/10 (which in turn advances the next one by 1/100 and so on). Some innovative early calculators, notably Chebyshev calculator from 1870, [ 10 ] and a design by Selling, [ 11 ] from 1886, used this method, but neither were successful.

  3. Arithmetic progression - Wikipedia

    en.wikipedia.org/wiki/Arithmetic_progression

    The product of the members of a finite arithmetic progression with an initial element a 1, common differences d, and n elements in total is determined in a closed expression a 1 a 2 a 3 ⋯ a n = a 1 ( a 1 + d ) ( a 1 + 2 d ) . . .

  4. Summation - Wikipedia

    en.wikipedia.org/wiki/Summation

    The summation of an explicit sequence is denoted as a succession of additions. For example, summation of [1, 2, 4, 2] is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. Because addition is associative and commutative, there is no need for parentheses, and the result is the same irrespective of the order of the summands ...

  5. Integer sequence - Wikipedia

    en.wikipedia.org/wiki/Integer_sequence

    An integer sequence is computable if there exists an algorithm that, given n, calculates a n, for all n > 0. The set of computable integer sequences is countable.The set of all integer sequences is uncountable (with cardinality equal to that of the continuum), and so not all integer sequences are computable.

  6. 100 Envelope Challenge: How To Save $5,000 in 100 Days - AOL

    www.aol.com/100-envelope-challenge-save-5...

    Download a 100 envelope challenge printable tracker with the numbers 1 to 100 on it. Use an online random number generator to pick the daily random numbers that equate to the amount of money to save.

  7. Harshad number - Wikipedia

    en.wikipedia.org/wiki/Harshad_number

    The number 18 is a harshad number in base 10, because the sum of the digits 1 and 8 is 9, and 18 is divisible by 9.; The Hardy–Ramanujan number (1729) is a harshad number in base 10, since it is divisible by 19, the sum of its digits (1729 = 19 × 91).

  8. Polite number - Wikipedia

    en.wikipedia.org/wiki/Polite_number

    A Young diagram representing visually a polite expansion 15 = 4 + 5 + 6. In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers.

  9. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    As an illustration of this, the parity cycle (1 1 0 0 1 1 0 0) and its sub-cycle (1 1 0 0) are associated to the same fraction ⁠ 5 / 7 ⁠ when reduced to lowest terms. In this context, assuming the validity of the Collatz conjecture implies that (1 0) and (0 1) are the only parity cycles generated by positive whole numbers (1 and 2 ...