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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 suma_k and sumb_k be two series with positive terms and suppose lim_(k->infty)(a_k)/(b_k)=rho. If rho is finite and rho>0, then the two series both converge or diverge.

Let N be an odd integer, and assume there exists a Lucas sequence {U_n} with associated Sylvester cyclotomic numbers {Q_n} such that there is an n>sqrt(N) (with n and N ...

Let {a_n} be a series of positive terms with a_(n+1)<=a_n. Then sum_(n=1)^(infty)a_n converges iff sum_(k=0)^infty2^ka_(2^k) converges.

D = f_(xx)f_(yy)-f_(xy)f_(yx) (1) = f_(xx)f_(yy)-f_(xy)^2, (2) where f_(ij) are partial derivatives.

A test to determine if a given series converges or diverges.

Let {u_n(x)} be a sequence of functions. If 1. u_n(x) can be written u_n(x)=a_nf_n(x), 2. suma_n is convergent, 3. f_n(x) is a monotonic decreasing sequence (i.e., ...

A robust estimation based on a rank test.

The probability that a statistical test will be positive for a true statistic.

The probability that a statistical test will be negative for a negative statistic.