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Introduction to Power Series definitions

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  • Sequence
    An ordered list of numbers generated by a specific formula, where each entry corresponds to a particular value of a variable.
  • Term
    A single entry in an ordered list, calculated by substituting a specific value into a given formula.
  • Factorial
    A product of all positive integers up to a given number, with zero yielding a value of one by definition.
  • Zero Factorial
    A special case in mathematics where the product of no numbers is defined as one.
  • Formula
    A mathematical expression that provides a rule for calculating each entry in an ordered list.
  • Index
    A variable, often represented by n, that identifies the position of an entry within an ordered list.
  • Substitution
    The process of replacing a variable in a mathematical expression with a specific value to compute a result.
  • Power
    A mathematical operation involving repeated multiplication of a number by itself, as seen in squared values.
  • Product
    The result of multiplying two or more numbers or expressions together.
  • Natural Number
    A positive integer used to count positions or calculate entries in ordered lists.
  • Ordered List
    A collection of numbers arranged in a specific sequence, each associated with a unique position.
  • Calculation
    A step-by-step process of simplifying expressions to determine specific values in a mathematical context.
  • Expression
    A combination of numbers, variables, and operations that represents a mathematical relationship.
  • Position
    The specific place of an entry within an ordered list, typically determined by the index.
  • Value
    A numerical result obtained after performing all required operations in a mathematical expression.