Andoza:Series (mathematics) sahifasining manbasini koʻrish

{{Navbox
| name  = Series (mathematics)
| title = [[Sequence]]s and [[Series (mathematics)|series]]
| state = {{{state|}}}
| image = [[File:Fibonacci spiral 34.svg|80px|link=Fibonacci sequence|alt=Fibonacci spiral with square sizes up to 34.]]
| listclass = hlist
| above = [[List of mathematical series|List of mathematical series]]
| group1 = [[Integer sequence|Integer sequences]]
| list1 = <!--
-->{{Navbox|subgroup
  | groupstyle = text-align:left
  | group1 = Basic
  | list1  = 
* [[Arithmetic progression]]
* [[Geometric progression]]
* [[Harmonic progression (mathematics)|Harmonic progression]]
* [[Square number]]
* [[Cube (algebra)|Cubic number]]
* [[Factorial]]
* [[Power of two|Powers of two]]
* [[Power of three|Powers of three]] 
* [[Power of 10|Powers of 10]]

   | group2 = Advanced {{nobold|1=([[List of OEIS sequences|list]])}}
   | list2  = 
* [[Complete sequence]]
* [[Fibonacci sequence]]
* [[Figurate number]]
* [[Heptagonal number]]
* [[Hexagonal number]]
* [[Lucas number]]
* [[Pell number]]
* [[Pentagonal number]]
* [[Polygonal number]]
* [[Triangular number]]
** [[Triangular array|array]]

}}<!-- END: Navbox|subgroup (group1) -->

| group2 = Properties of sequences
| list2  = 
* [[Cauchy sequence]]
* [[Monotonic function]]
* [[Periodic sequence]]

| group3 = Properties of series
| list3  =

{{Navbox|subgroup
  | groupstyle = text-align:left
  | group1 = Series
  | list1  =
* [[Alternating series|Alternating]]
* [[Convergent series|Convergent]] 
* [[Divergent series|Divergent]]
* [[Telescoping series|Telescoping]]
  | group2 = Convergence
  | list2  =

* [[Absolute convergence|Absolute]]
* [[Conditional convergence|Conditional]]
* [[Uniform convergence|Uniform]]
}}

| group4 = Explicit series
| list4  = {{Navbox|subgroup
  | groupstyle = text-align:left
  | group1 = Convergent
  | list1  =
* [[1/2 − 1/4 + 1/8 − 1/16 + ⋯]]
* [[1/2 + 1/4 + 1/8 + 1/16 + ⋯]]
* [[1/4 + 1/16 + 1/64 + 1/256 + ⋯]]
* [[Riemann zeta function|1 + 1/2<sup>''s''</sup> + 1/3<sup>''s''</sup> + ... (Riemann zeta function)]]
* [[Arithmetico-geometric sequence|Arithmetico-geometric]]
* [[Binomial series|Binomial]]

  | group2 = Divergent
  | list2  =
*     [[1 + 1 + 1 + 1 + ⋯]]
*     [[Grandi's series|1 − 1 + 1 − 1 + ⋯ (Grandi's series)]]
*     [[1 + 2 + 3 + 4 + ⋯]]
*     [[1 − 2 + 3 − 4 + ⋯]]
*     [[1 + 2 + 4 + 8 + ⋯]]
*     [[1 − 2 + 4 − 8 + ⋯]]
*     [[Infinite arithmetic series]]
*     [[1 − 1 + 2 − 6 + 24 − 120 + ⋯|1 − 1 + 2 − 6 + 24 − 120 + ⋯ (alternating factorials)]]
*     [[Harmonic series (mathematics)|1 + 1/2 + 1/3 + 1/4 + ⋯ (harmonic series)]]
*     [[Divergence of the sum of the reciprocals of the primes|1/2 + 1/3 + 1/5 + 1/7 + 1/11 + ⋯ (inverses of primes)]]
}}<!-- END: Navbox|subgroup (group4) -->

| group5 = Kinds of series
| list5 =
* [[Geometric series|Geometric]]
* [[Taylor series]]
* [[Power series]]
* [[Formal power series]]
* [[Laurent series]]
* [[Puiseux series]]
* [[Dirichlet series]]
* [[Trigonometric series]]
* [[Fourier series]]
* [[Generating series]]

| group6 = Tests of convergence
| list6 =
* [[Abel's test|Abel's]]
* [[Alternating series test|Alternating series]]
* [[Cauchy condensation test|Cauchy condensation]]
* [[Direct comparison test|Direct comparison]]
* [[Dirichlet's test|Dirichlet's]]
* [[Integral test for convergence|Integral]]
* [[Limit comparison test|Limit comparison]]
* [[Ratio test|Ratio]]
* [[Root test|Root]]
* [[Term test|Term]]

| group7 = [[Hypergeometric function|Hypergeometric series]]
| list7 =
* [[Generalized hypergeometric series]]
* [[Hypergeometric function of a matrix argument]]
* [[Lauricella hypergeometric series]]
* [[Modular hypergeometric series]]
* [[Riemann's differential equation]]
* [[Theta hypergeometric series]]<!-- GOTCHA: }} -->

| belowclass = hlist
| below = 
* {{icon|Category}} [[:Category:Series (mathematics)|Category]]

}}<!-- END: Navbox --><noinclude>
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==See also==
*{{tl|Sequence}}
*{{tl|Classes of natural numbers}}
*{{tl|Prime number classes}}
*{{tl|Fractals}}
*{{tl|Calculus topics}}

[[Category:Mathematical Analysis navigational boxes|Geometric series]]

}}
</noinclude>