Editing List of real analysis topics (section)

===[[Sequence]]s and [[Series (mathematics)|series]]===
(''see also [[list of mathematical series]]'')

*[[Arithmetic progression]] – a sequence of numbers such that the difference between the consecutive terms is constant
**[[Generalized arithmetic progression]] –  a sequence of numbers such that the difference between consecutive terms can be one of several possible constants
*[[Geometric progression]] – a sequence of numbers such that each consecutive term is found by multiplying the previous one by a fixed non-zero number
*[[Harmonic progression (mathematics)|Harmonic progression]] –  a sequence formed by taking the reciprocals of the terms of an arithmetic progression
*'''Finite sequence''' – ''see [[sequence]]''
*'''Infinite sequence''' – ''see [[sequence]]''
*'''Divergent sequence''' – ''see [[limit of a sequence]] or [[divergent series]]''
*'''Convergent sequence''' – ''see [[limit of a sequence]] or [[convergent series]]''
**[[Cauchy sequence]] – a sequence whose elements become arbitrarily close to each other as the sequence progresses
*[[Convergent series]] – a series whose sequence of partial sums converges
*[[Divergent series]] – a series whose sequence of partial sums diverges
*[[Power series]] – a series of the form <math>f(x) = \sum_{n=0}^\infty a_n \left( x-c \right)^n = a_0 + a_1 (x-c)^1 + a_2 (x-c)^2 + a_3 (x-c)^3 + \cdots</math>
**[[Taylor series]] – a series of the form <math>f(a)+\frac {f'(a)}{1!} (x-a)+ \frac{f''(a)}{2!} (x-a)^2+\frac{f^{(3)}(a)}{3!}(x-a)^3+ \cdots. </math>
***'''Maclaurin series''' – ''see [[Taylor series]]''
****[[Binomial series]] – the Maclaurin series of the function ''f'' given by ''f''(''x'')&nbsp;''=''&nbsp;(1&nbsp;+&nbsp;''x'')<sup>&nbsp;''&alpha;''</sup>
*[[Telescoping series]]
*[[Alternating series]]
*[[Geometric series]]
**[[Divergent geometric series]]
*[[Harmonic series (mathematics)|Harmonic series]]
*[[Fourier series]]
*[[Lambert series]]

====[[Summation]] methods====

*[[Cesàro summation]]
*[[Euler summation]]
*[[Lambert summation]]
*[[Borel summation]]
*[[Summation by parts]] – transforms the summation of products of into other summations
*[[Cesàro mean]]
*[[Abel's summation formula]]

====More advanced topics====

*[[Convolution]]
**[[Cauchy product]] –is the discrete convolution of two sequences
*[[Farey sequence]] – the sequence of [[completely reduced fraction]]s between 0 and 1
*[[Oscillation (mathematics)|Oscillation]] – is the behaviour of a sequence of real numbers or a real-valued function, which does not converge, but also does not diverge to +∞ or −∞; and is also a quantitative measure for that.
*[[Indeterminate form]]s – algebraic expressions gained in the context of limits. The indeterminate forms include 0<sup>0</sup>, 0/0, 1<sup>∞</sup>, ∞&nbsp;&minus;&nbsp;∞, ∞/∞,  0&nbsp;×&nbsp;∞, and ∞<sup>0</sup>.