Geometric series - Wikipedia
In mathematics, a geometric series is a series summing the terms of an infinite geometric sequence, in which the ratio of consecutive terms is constant. For example, the series is a geometric series with common ratio , which converges to the sum of .
Geometric Series - Formula, Examples, Convergence - Cuemath
A geometric series is the sum of finite or infinite terms of a geometric sequence. For the geometric sequence a, ar, ar 2 , ..., ar n-1 , ..., the corresponding geometric series is a + ar + ar 2 + ..., ar n-1 + ....
等比数列 - 维基百科，自由的百科全书
一個等比數列的首 項之和，稱為等比数列和（sum of geometric sequence）或幾何級數（geometric series），記作 。 舉例來說，等比數列 {,,,} 的和是 + + + = 。 等比數列求和的公式如下：
Geometric Series -- from Wolfram MathWorld
5 天之前 · A geometric series is a series for which the ratio of each two consecutive terms is a constant function of the summation index . The more general case of the ratio a rational function of the summation index produces a series called a hypergeometric series .
幾何級數 - 维基百科，自由的百科全书
在数学中，几何级数（英語： Geometric series ）是无穷多个项的总和，这些连续项之间的公比是恒定的。 例如， 该数列 1 2 + 1 4 + 1 8 + 1 16 + ⋯ {\displaystyle {\frac {1}{2}}\,+\,{\frac {1}{4}}\,+\,{\frac {1}{8}}\,+\,{\frac {1}{16}}\,+\,\cdots }
9.3: Geometric Sequences and Series - Mathematics LibreTexts
2024年3月22日 · A geometric sequence is a sequence where the ratio \(r\) between successive terms is constant. The general term of a geometric sequence can be written in terms of its first term \(a_{1}\), common ratio \(r\), and index \(n\) as follows: \(a_{n} = a_{1} r^{n−1}\). A geometric series is the sum of the terms of a geometric sequence.
Geometric Series | Formula, Derivation, Geometric Mean
2024年11月4日 · A geometric series is a sequence of numbers in which each term after the first is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio.
2023年10月15日 · Historically, the geometric series first appeared in Zeno’s paradox. Assume Archilles races a turtle who is given an advance of a = 1 miles Assume the turtle can run r times slower than Archilles. Both start running. Once Archilles reaches the start point of the turtle, the turtle is x miles ahead at S1 = 1 + r.
Geometric series - Math.net
A geometric series is the sum of a geometric sequence with an infinite number of terms. Briefly, a geometric sequence is a type of sequence in which each subsequent term after the first term is determined by multiplying the previous term by a constant (not equal to 1).
The advice in the text is: Learn the geometric series. This is the most important series and also the simplest. The pure geometric series starts with the constant term 1: 1+x +x2 +... = A.With other symbols C z oP = &.The ratio between terms is x (or r). Convergence requires 1x1 < 1(or Irl < 1). ox +ax2 + -.= &.