Search results
Results from the WOW.Com Content Network
In the second step, they were divided by 3. The final result, 4 / 3 , is an irreducible fraction because 4 and 3 have no common factors other than 1. The original fraction could have also been reduced in a single step by using the greatest common divisor of 90 and 120, which is 30. As 120 ÷ 30 = 4, and 90 ÷ 30 = 3, one gets
Unit fractions can also be expressed using negative exponents, as in 2 −1, which represents 1/2, and 2 −2, which represents 1/(2 2) or 1/4. A dyadic fraction is a common fraction in which the denominator is a power of two , e.g. 1 / 8 = 1 / 2 3 .
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.
Name First elements Short description OEIS Mersenne prime exponents : 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ... Primes p such that 2 p − 1 is prime.: A000043 ...
2/9: 1/3: 4/9: 0 7/24: 1/4: 1/3: ... The simplest method from this class is the order 2 implicit ... by considering Lobatto coefficients of the form , (,,) =, +, + ...
The first four partial sums of 1 + 2 + 4 + 8 + ⋯. In mathematics, 1 + 2 + 4 + 8 + ⋯ is the infinite series whose terms are the successive powers of two. As a geometric series, it is characterized by its first term, 1, and its common ratio, 2. As a series of real numbers it diverges to infinity, so the sum of this series is infinity.
4/3: −5/2: 4/3: −1/12: 6 1/90: −3/20: 3/2: −49/18: 3/2: −3/20: 1/90: 8 −1/560: 8/315: ... The order of accuracy of the approximation takes the usual form
(4 4/3 ∞), (3/2 3 ∞), (6 6/5 ∞), (3 3/2 ∞). Branko Grünbaum and G. C. Shephard , in the 1987 book Tilings and patterns , section 12.3, enumerate a list of 25 uniform tilings, including the 11 convex forms, and add 14 more they call hollow tilings , using the first two expansions above: star polygon faces and generalized vertex figures.