SeriesEdit
A series is the sum of the terms of a sequence.
 Finite sequences and series have defined first and last terms, whereas
 infinite sequences and series continue indefinitely
The sum of terms of a sequence is a series. More precisely, if (x_{1}, x_{2}, x_{3}, ...) is a sequence, one may consider the sequence of partial sums (S_{1}, S_{2}, S_{3}, ...), with
Sums of powersEdit
Power seriesEdit
Infinite sum (for )  Finite sum  

where and  
where Li_{s}(x) is the polylogarithm of x. 
Simple denominatorsEdit
Factorial denominatorsEdit
Many power series which arise from Taylor's theorem have a coefficient containing a factorial.
 (c.f. mean of Poisson distribution)
 (c.f. second moment of Poisson distribution)
Modifiedfactorial denominatorsEdit
 ^{[1]}
 ^{[1]}
 ^{[1]}
Binomial seriesEdit

 with generalized binomial coefficients
 with generalized binomial coefficients
Miscellaneous:
 ^{[2]}
 ^{[2]}
 ^{[2]}
 ^{[2]}
Bernoulli NumbersEdit
 ^{[1]}
 ^{[1]}
 ^{[1]}
 ^{[1]}
Harmonic NumbersEdit
 ^{[1]}
 ^{[1]}
 ^{[1]}
Binomial coefficientsEdit
Trigonometric functionsEdit
Sums of sines and cosines arise in Fourier series.