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where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = 1 / 6 , B 4 = − + 1 / 30 , and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]
Lucas numbers have L 1 = 1, L 2 = 3, and L n = L n−1 + L n−2. Primefree sequences use the Fibonacci recursion with other starting points to generate sequences in which all numbers are composite. Letting a number be a linear function (other than the sum) of the 2 preceding numbers. The Pell numbers have P n = 2P n−1 + P n−2.
Petar II Petrović-Njegoš was born Radivoje "Rade" Petrović on 13 November [ O.S. 1 November] 1813 in the mountain village of Njeguši, near Cetinje. [ nb 1] His father, Tomislav "Tomo" Petrović ( b. 1762–63), was a member of the Petrović clan of the Njeguši tribe of Katuni nahiya. Njegoš's mother, Ivana Proroković, hailed from the ...
The idea becomes clearer by considering the general series 1 − 2x + 3x 2 − 4x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1.
1/2 + 1/4 + 1/8 + 1/16 + ⋯. First six summands drawn as portions of a square. The geometric series on the real line. In mathematics, the infinite series 1 2 + 1 4 + 1 8 + 1 16 + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. In summation notation ...
Infobox references. 1,1,1,2,2,3,3-Heptachloropropane is a compound of chlorine, hydrogen, and carbon. [1] Its linear formula is C 2 Cl 5 CHCl 2. [2] Heptachloropropane is made in a modified Friedel-Crafts or Prins reaction from chloroform and tetrachloroethylene with catalytic aluminum chloride. Dehydrochlorination with a base gives ...
This is a list of articles about prime numbers.A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers.
This is a list of emoticons or textual portrayals of a writer's moods or facial expressions in the form of icons. Originally, these icons consisted of ASCII art, and later, Shift JIS art and Unicode art. In recent times, graphical icons, both static and animated, have joined the traditional text-based emoticons; these are commonly known as ...