In mathematics, a geometric series is a series with a constant ratio between successive terms. For example, the series
is geometric, because each successive term can be obtained by multiplying the previous term by 1 / 2.
Geometric series are one of the simplest examples of infinite series with finite sums, although not all of them have this property. Historically, geometric series played an important role in the early development of calculus, and they continue to be central in the study of convergence of series. Geometric series are used throughout mathematics, and they have important applications in physics, engineering, biology, economics, computer science, queueing theory, and finance.
Read more about Geometric Series: Common Ratio, Sum
Famous quotes containing the words geometric and/or series:
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o’ th’ day
The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)
“Galileo, with an operaglass, discovered a more splendid series of celestial phenomena than anyone since.”
—Ralph Waldo Emerson (1803–1882)