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Pairing up the terms of the series 1 / 2 − 1 / 4 + 1 / 8 − 1 / 16 + ⋯ results in another geometric series with the same sum, 1 / 4 + 1 / 16 + 1 / 64 + 1 / 256 + ⋯. This series is one of the first to be summed in the history of mathematics ; it was used by Archimedes circa 250–200 BC.
For the leptons, the gauge group can be written SU(2) l × U(1) L × U(1) R. The two U(1) factors can be combined into U(1) Y × U(1) l where l is the lepton number. Gauging of the lepton number is ruled out by experiment, leaving only the possible gauge group SU(2) L × U(1) Y. A similar argument in the quark sector also gives the same result ...
Ray J's 1997 debut single, "Let It Go", was released by EastWest Records for the soundtrack to the F. Gary Gray film, Set It Off. Both moderate hits, the song peaked within the top 40 of the Billboard Hot 100 and additionally served as the lead single for Ray J's debut studio album, Everything You Want (1997), which entered the Top R&B/Hip-Hop ...
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2. “Watch Me”. “This cue is crucial to teach because if your dog is taught to focus on you and watch you, they will be less likely distracted by the world around them, or frustrated that ...
The case n = 2 is the axiom of pairing with A = A 1 and B = A 2. The cases n > 2 can be proved using the axiom of pairing and the axiom of union multiple times. For example, to prove the case n = 3, use the axiom of pairing three times, to produce the pair {A 1,A 2}, the singleton {A 3}, and then the pair {{A 1,A 2},{A 3}}. The axiom of union ...
The e-commerce giant's capital investments - mostly for building cloud and generative AI infrastructure - is expected to have risen 43% in the second quarter to $16.41 billion, according to LSEG data.
The 37.5 mm length is not derived by a certain scale ratio. While HO scale is a 1:87 scale (3.5 mm to 1 foot), resulting in a 16.5 mm ( 0.65 in) gauge from real life prototype 1,435 mm ( 4 ft 81⁄2 in) standard gauge standard gauge. Conversely, modeling standard gauge in Lego trains would yield a scaling of (37.5:1435 =) 1:38.3.