1 + 2 + 4 + 8 + ⋯ that and , but the underlying proofs demand careful thinking about the interpretation of endless sums. It is also possible to view this series as convergent in a number system different from the real numbers, namely, the 2-adic numbers. As a series of 2-adic numbers this series converges to the same sum, −1, as was derived above by analytic continuation. 1 + 2 + 4 + 8 + ⋯ In mathematics, 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.
2-8-8-2 still used on steel mill lines and other railroads until 1983. Other equivalent classifications are: UIC classification: 1DD1 (also known as German classification and Italian classification) French classification: 140+041 Turkish classification: 45+45 Swiss classification: 4/5+4/5 The first 2-8-8-2 was built in 1909 by Baldwin, who sold two to the Southern Pacific Railroad (classified MC-1), and then three each to the Union Pacific Railroad and UP-owned Oregon Railroad and Navigation Company. Baldwin conceived the type as an expansion of the 2-6-6-2 permitting a greater tractive effort. The next order for the type was from the Southern Pacific; these differed in being