2-8-4 across the Berkshire mountains was a substantial test for the new locomotives and, as a result, the name "Berkshire" was adopted for the locomotive type. In Europe, 2-8-4 tender locomotives were designed mainly for passenger express trains, but they also hauled long distance express freights to increase utilisation. European 2-8-4 tank locomotives were a logical transition from the 2-8-2T locomotive types, allowing larger fireboxes and larger coal bunkers. They were mainly used for busy suburban services in heavily populated suburban areas of big cities, but infrequently also for sparsely populated rural areas or long distance lines. The Western Australian K-class
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