finite

Examples of finite in the following topics:

• Summing Terms in an Arithmetic Sequence

  • An arithmetic sequence which is finite has a specific formula for its sum.
  • The sum of the members of a finite arithmetic sequence is called an arithmetic series.
  • We can come up with a formula for the sum of a finite arithmetic formula by looking at the sum in two different ways.
  • Even if one is dealing with an infinite sequence, the sum of that sequence can still be found up to any $n$th term with the same equation used in a finite arithmetic sequence.

• Infinite Geometric Series

  • Geometric series are one of the simplest examples of infinite series with finite sums.
  • If the terms of a geometric series approach zero, the sum of its terms will be finite.
  • A geometric series with a finite sum is said to converge.
  • What follows in an example of an infinite series with a finite sum.
  • If a series converges, we want to find the sum of not only a finite number of terms, but all of them.

• Introduction to Sequences

  • Sequences can be finite, as in this example, or infinite, such as the sequence of all even positive integers $(2, 4, 6, \cdots )$.
  • Finite sequences are sometimes known as strings or words and infinite sequences as streams.
  • A more formal definition of a finite sequence with terms in a set $S$ is a function from $\left \{ 1, 2, \cdots, n \right \}$ to $S$ for some $n > 0$.
  • A sequence of a finite length n is also called an $n$-tuple.
  • Finite sequences include the empty sequence $( \quad )$ that has no elements.

• What is a Quadratic Function?

  • The constants $b$and $c$ can take any finite value, and $a$ can take any finite value other than $0$.

• What Are Polynomials?

  • A polynomial is a finite expression containing constants and variables connected only through basic operations of algebra.
  • A polynomial over $\mathbb{R}$ is a finite sum of monomials over $\mathbb{R}$.
  • is the finite sum of the $4$ monomials: $4x^{13}, 3x^2, -\pi x$ and $1 = 1x^0.$

• Applications of Geometric Series

  • Geometric series have applications in math and science and are one of the simplest examples of infinite series with finite sums.
  • Geometric series are one of the simplest examples of infinite series with finite sums, although not all of them have this property.
  • Zeno's mistake is in the assumption that the sum of an infinite number of finite steps cannot be finite.

• Zeroes of Polynomial Functions With Rational Coefficients

  • The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over.

• Difference Quotients

  • If |ΔP| is finite, meaning measurable, then ΔF(P) is known as a finite difference, with specific denotations of DP and DF(P).

• Interval Notation

  • Bounded intervals are also commonly known as finite intervals.

• Nonlinear Systems of Inequalities

  • Whereas a solution for a linear system of equations will contain an infinite, unbounded area (lines can only pass one another a maximum of once), in many instances, a solution for a nonlinear system of equations will consist of a finite, bounded area.