South African Class GEA 4-8-2+2-8-4 South African Class GEA 4-8-2+2-8-4 The South African Railways Class GEA 4-8-2+2-8-4 of 1946 was an articulated steam locomotive. During 1946 and 1947, the South African Railways placed fifty Class GEA Garratt articulated steam locomotives with a 4-8-2+2-8-4 Double Mountain type wheel arrangement in service. The Class GEA 4-8-2+2-8-4 Double Mountain type Garratt locomotive was the first new post-Second World War locomotive class to be introduced on the South African Railways (SAR). It was designed by Dr. M.M. Loubser, Chief Mechanical Engineer (CME) of the SAR from 1939 to 1949, and although it was a development of the Class GE
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