In mathematics, the nth-term test for divergence is a simple test for the divergence of an infinite series: If lim n → ∞ a n ≠ 0 {\displaystyle \lim _{n\to...

The test is inconclusive if the limit of the summand is zero. This is also known as the nth-term test, test for divergence, or the divergence test. This...

mathematics, taking the nth root is an operation involving two numbers, the radicand and the index or degree. Taking the nth root is written as x n {\displaystyle...

question either mechanically (every nth word) or selectively, depending on exactly what aspect it is intended to test for. The methodology is the subject...

PlanetMath Another proof that nth roots of integers are irrational, except for perfect nth powers by Scott E. Brodie The Rational Roots Test at purplemath.com...

figurate number, other examples being square numbers and cube numbers. The nth triangular number is the number of dots in the triangular arrangement with...

making his case for a test ban, Kennedy drew a direct link between continued testing and nuclear proliferation, calling it the "'Nth-country' problem." While...

and then cuts off the series after the T N {\displaystyle T_{N}} term, one gets an Nth-degree polynomial approximating f(x). The reason this polynomial...

construction of pentagonal numbers are not rotationally symmetrical. The nth pentagonal number pn is the number of distinct dots in a pattern of dots...

83 and 461. We can derive this test from the formula for the nth pentatope number. Given a positive integer x, to test whether it is a pentatope number...

global issues List of nuclear weapons List of states with nuclear weapons Nth Country Experiment Nuclear blackout Nuclear bunker buster Nuclear weapons...

The shifting nth root algorithm is an algorithm for extracting the nth root of a positive real number which proceeds iteratively by shifting in n digits...

the finite sums of the n first terms of the series, which are called the nth partial sums of the series. That is, ∑ i = 1 ∞ a i = lim n → ∞ ∑ i = 1 n...

pre-eminent engineering university, the Norwegian Institute of Technology (NTH) which was established by Parliament in 1910 as Norway's national engineering...

case, bn is called "b raised to the nth power", "b (raised) to the power of n", "the nth power of b", "b to the nth power", or most briefly as "b to the...

average, without speculating on global linkages; he never actually used the term "six degrees of separation". Since the Psychology Today article gave the...

be seen by examining the prime factors of the binomial coefficients: the nth binomial coefficient is ( p n ) = p ! n ! ( p − n ) ! . {\displaystyle {\binom...

terms of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations...

61, 91, 127, 169, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919. The nth centered hexagonal number is given by the formula H ( n ) = n 3 − ( n − 1...

terms are the natural numbers 1 + 2 + 3 + 4 + ⋯ is a divergent series. The nth partial sum of the series is the triangular number ∑ k = 1 n k = n ( n +...

arithmetico-geometric sequence is the product of the nth term of an arithmetic sequence and the nth term of a geometric one. Arithmetico-geometric sequences...

discussion of doomsday machines, Kahn raises the problem of a nuclear-armed Nth country triggering a doomsday machine, and states that he didn't advocate...

the table below, "na" is shorthand for the "nth rank, primary" (正n品), which is a higher sub-rank than "nth rank, secondary" (從n品), denoted as "nb" in the...

{1}{x}}e^{x}-\ln(x)e^{x}.\end{aligned}}} Here the second term was computed using the chain rule and the third term using the product rule. The known derivatives...

terms of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations...

revealed to Duke Thomas that the term "meta" originated from a rudimentary hospital program used to automatically flag Nth metal toxicity found in a person's...

x-c)+a_{2}(x-c)^{2}+\dots } where an represents the coefficient of the nth term and c is a constant. Power series are useful in mathematical analysis,...

f^{(6)}(x),\ldots .} This notation also makes it possible to describe the nth derivative, where n is a variable. This is written f ( n ) ( x ) . {\displaystyle...

term equation, ( a b ) c = a ( b c ) {\displaystyle (ab)c=a(bc)} , while the Cayley table shows 2-term products. However, Light's associativity test can...

arithmetic mean which uses their sum). The geometric mean is defined as the nth root of the product of n numbers, i.e., for a set of numbers x1, x2, ......