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Also known as the Leibniz criterion. An alternating series converges if a_1>=a_2>=... and lim_(k->infty)a_k=0.

Let sum_(k=0)^(infty)a_k=a and sum_(k=0)^(infty)c_k=c be convergent series such that lim_(k->infty)(a_k)/(c_k)=lambda!=0. Then ...

Euler's series transformation is a transformation that sometimes accelerates the rate of convergence for an alternating series. Given a convergent alternating series with sum ...

In combinatorial mathematics, the series-parallel networks problem asks for the number of networks that can be formed using a given number of edges. The edges can be ...

_2F_1(-1/2,-1/2;1;h^2) = sum_(n=0)^(infty)(1/2; n)^2h^(2n) (1) = 1+1/4h^2+1/(64)h^4+1/(256)h^6+... (2) (OEIS A056981 and A056982), where _2F_1(a,b;c;x) is a hypergeometric ...

The log-series distribution, also sometimes called the logarithmic distribution (although this work reserves that term for a distinct distribution), is the distribution of ...

If the difference between the order and the dimension of a series is less than the curve genus, then the series is special.

Like the entire harmonic series, the harmonic series sum_(k=1)^infty1/(p_k)=infty (1) taken over all primes p_k also diverges, as first shown by Euler in 1737 (Nagell 1951, ...

A series-reduced tree is a tree in which all nodes have degree other than 2 (in other words, no node merely allows a single edge to "pass through"). Series-reduced trees are ...

Trigonometric identities which prove useful in the construction of map projections include (1) where A^' = A-C (2) B^' = 2B-4D (3) C^' = 4C (4) D^' = 8D. (5) ...