South African Class 4 4-8-2 South African Class 4 4-8-2 The South African Railways Class 4 4-8-2 of 1911 was a steam locomotive from the pre-Union era in the Cape of Good Hope. In 1911, the Cape Government Railways placed two steam locomotives with a Mountain type wheel arrangement in service. They were renumbered and designated Class 4 when they were assimilated into the South African Railways a year later. The first Mountain type locomotive of the Cape Government Railways (CGR) was designed as a heavy mixed traffic engine at the Salt River shops by H.M. Beatty, the Chief Locomotive Superintendent of the CGR from
1/2 + 1/4 + 1/8 + 1/16 + ⋯ 1/2 + 1/4 + 1/8 + 1/16 + ⋯ In mathematics, the infinite series is an elementary example of a geometric series that converges absolutely. There are many different expressions that can be shown to be equivalent to the problem, such as the form: 2 + 2 + 2 + ... The sum of this series can be denoted in summation notation as: As with any infinite series, the infinite sum is defined to mean the limit of the sum of the first terms as approaches infinity. Multiplying by 2 reveals a useful relationship: Subtracting from both sides, As approaches