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  • ...one before it, every term of a geometric sequence can be expressed as the sum of the first term and a multiple of the common ratio. Let <math>a_1</math> == Sum ==
    4 KB (649 words) - 20:09, 19 July 2024
  • == Sum of Fourth Powers == ...he continued fraction and <math>C_k=P_k/Q_k</math> is the <math>k</math>th convergent, all solutions to the Pell equation are in the form <math>(P_{ia},Q_{ia})</
    9 KB (1,434 words) - 00:15, 4 July 2024
  • ...ums neatly and compactly. Besides being easier to write than the explicit sum, sigma notation is also useful in that it shows the general form of each ad ...> defined on the integers, we write <math>\sum_{k=m}^n a(k)</math> for the sum <math>a(m)+a(m+1)+a(m+2)+\ldots+a(n-1)+a(n)</math>.
    2 KB (335 words) - 16:17, 8 February 2024
  • A '''series''' is a sum of consecutive terms in a [[sequence]]. Common series are based on common * [[Convergent|Convergence]]
    400 bytes (43 words) - 20:21, 22 July 2021
  • ...ive function]]. The relationship between the product of the primes and the sum of the natural numbers makes it immediately obvious that the [[Riemann zeta
    708 bytes (116 words) - 20:15, 13 August 2015
  • <center><math>\left[n\right]-\sum\left[\frac{n}{a_1}\right]+\sum\left[\frac{n}{a_1a_2}\right]-\ldots</math>.</center> <center><math>\phi(n)=n-\sum\left[\frac{n}{p}\right]+\sum\left[\frac{n}{pp'}\right]-\ldots=n\prod_{p|n}\left(1-\frac{1}{p}\right)</ma
    5 KB (910 words) - 01:58, 1 March 2022
  • The sum of an infinite geometric series is a positive number <math>S</math>, and th ...>a\cdot r = 1</math> and we wish to find the minimum value of the infinite sum of the series. We know that: <math>S_\infty = \frac{a}{1-r}</math> and sub
    7 KB (1,284 words) - 00:12, 10 November 2024
  • ...y\frac{1}{k^a}</math> is convergent; let <math>L</math> be the sum of this convergent series. Let <math>I\subset \mathbb{R}</math> be the interval <math>[-L,L]</ ...he total length <math>\mu(U_0\cup \cdot\cup U_{m-1})</math> is at most the sum of the lengths <math>\mu(U_0)+\cdots+\mu(U_{m-1})=\frac{2}{m^a}+\frac{2}{(m
    6 KB (1,068 words) - 02:20, 24 January 2024
  • A convergent sum is a sum that converges to a quantity, for example a arithmetic sequence that is non
    149 bytes (24 words) - 21:39, 5 March 2020