# 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.

## Series and Sequence Equations

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