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  • ...pointwise if at every point in the domain, the functions converge. Uniform convergence is a stronger condition, because (speaking informally) the function has to ...egin{cases} 1, & x = 1 \0, & \text{otherwise}\end{cases}</math>, but this convergence is ''not'' uniform.
    4 KB (622 words) - 18:20, 3 March 2010

Page text matches

  • ==Convergence== A classic example of convergence would be to show that <math>1/n\to 0</math> as <math>n\to \infty</math>.
    2 KB (413 words) - 20:18, 13 November 2022
  • ...us; thus, such a proof is beyond the scope of this article. If one assumes convergence, there is an elementary proof of the formula that uses [[Telescoping series
    4 KB (649 words) - 20:09, 19 July 2024
  • ==Proof of convergence==
    4 KB (830 words) - 17:48, 12 October 2006
  • *[[Convergence]]
    3 KB (452 words) - 22:17, 4 January 2021
  • ...le of radius 1 centered at (0,0). This is often referred to as a [[disk of convergence]]. Inside the disk, this particular function is equal to <math>\frac{a}{1-n
    1 KB (180 words) - 19:12, 19 August 2015
  • its radius of convergence is the greatest lower bound of the distance and its radius of convergence is the greatest quantity <math>R</math> for which
    9 KB (1,537 words) - 20:04, 26 July 2017
  • * [[Convergence]]
    2 KB (335 words) - 16:17, 8 February 2024
  • * [[Convergent|Convergence]]
    400 bytes (43 words) - 20:21, 22 July 2021
  • ...math>\sum_{i=0}^{\infty} (-1)^ia_i</math> satisfies the the above test for convergence. Then letting <math>\sum_{i=0}^{\infty} (-1)^ia_i</math> equal <math>S</mat
    2 KB (301 words) - 21:13, 19 February 2022
  • ...at primarily deals with definitions and theorems concerning continuity and convergence. Analysis covers a wide variety of topics which appear quite different to e ...ning analysis class; ideas such as continuity, connectedness, compactness, convergence,etc. Also included under this umbrella are modern integration theories (suc
    2 KB (352 words) - 17:12, 8 February 2015
  • ...pointwise if at every point in the domain, the functions converge. Uniform convergence is a stronger condition, because (speaking informally) the function has to ...egin{cases} 1, & x = 1 \0, & \text{otherwise}\end{cases}</math>, but this convergence is ''not'' uniform.
    4 KB (622 words) - 18:20, 3 March 2010
  • ...\sum_{i=1}^{\infty}\frac{5}{8^n}\right) \ &= 1-\frac{5}{7} \text{ (by the convergence of a geometric series)} \ &=\frac{2}{7}\end{align*}</cmath>
    920 bytes (134 words) - 12:06, 22 July 2024
  • ...the [[absolute value]] metric. It is also useful to give formal proofs of convergence for certain sequences.
    1 KB (216 words) - 16:53, 29 February 2020
  • ===Convergence===
    7 KB (1,280 words) - 11:39, 9 December 2022
  • ...are studied in the real numbers are the construction of the real numbers, convergence of sequences, subsets of the plane as metric spaces, limits, notions of [[c ...n to the convergence and divergence of sequences. Intuitively, the idea of convergence is captured by the notion that the sequence "approaches" some value as <mat
    9 KB (1,409 words) - 01:41, 30 May 2023
  • converges. We have to prove uniform convergence though, so back to work. Notice that this result above implies that there
    8 KB (1,471 words) - 21:02, 12 April 2022
  • ===Convergence of the sum of error terms===
    3 KB (543 words) - 16:32, 19 September 2022