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Series and Sequence

A series is the value (sum) obtained  when all the terms of a sequence are added up.  For example, "1, 2, 3, 4" is a sequence, with terms "1", "2", "3", and "4"; the corresponding series is the sum "1 + 2 + 3 + 4", and the value of the series is 10.

A sequence, aka progression, is an ordered list of numbers. The numbers in this ordered list are called "elements" or "terms". 

While some sequences are simply random values, other sequences have a definite pattern that is used to arrive at the sequence's terms. Two such sequences are the arithmetic and geometric sequences.
An  arithmetic sequence is one that has  a sequence of values follows a pattern of adding a fixed or constant amount from one term to the next. 

vCalc's Series and Sequence  contains equations that compute the sum of the terms of a sequence.

Parent Categories:

Series and Sequence Equations

  • `sum_(k=1)^n1/([p + (k-1)q](p+kq))` by vCalc
  • `sum_(k=1)^naq^(k-1)` by vCalc
  • `sum_(k=1)^nk^p` by vCalc
  • `sum_(x=0)^n(r^x sin(x alpha))` by vCalc
  • `sum_(x=1)^n cos(x alpha)` by vCalc
  • `sum_(x=1)^n sin(x alpha)` by vCalc
  • `sum_(x=1)^n x` by vCalc
  • `sum_(x=1)^n(2x-1)` by vCalc
  • `sum_(x=1)^n(a +(x-1)d)` by vCalc
  • `sum_(x=1)^n(x^2)` by vCalc
  • `sum_(x=1)^n(x^3)` by vCalc
  • `sum_(x=1)^n(x^4)` by vCalc
  • Arithmetic Series- Alternative Sum-of-Terms Formula by vCalc
  • Arithmetic Series-Last Term Formula_Copy by vCalc
  • Fibonacci Term by vCalc
  • Sum of Infinite Geometric Series_Copy by vCalc
  • Table of Integrals, Series and Products, 0dot14 - 2 by vCalc
  • `sum_(k=0) ^ (n-1) (a+kr)` by MichaelBartmess
  • `sum_(x=0)^n(r^x cos(x alpha))` by KurtHeckman
  • Fibonacci Sequence by MichaelBartmess
  • Golden Ratio Sequence by MichaelBartmess
  • Infinite Geometric Series by CalebSvobodny
  • Liouville's Number by MichaelBartmess
  • Sum_014-3 by MichaelBartmess
  • Sum_014-4 by MichaelBartmess
  • Sum_0_142 by MichaelBartmess