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The sum of an infinite G.P. . Is 6 and i...

The sum of an infinite G.P. . Is 6 and its first term is 2 . Find the series

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` S_(oo) = 6 = (a)/(1-r) and a = 2 `
` therefore (2)/(1-r) = 6`
` rArr 1 - r = (1)/(3)`
` rArr r = 1 (1)/(3) = (2)/(3)`
The required series is
` 2 + (4)/(3) + (8)/(9) + (16)/(27) + …`
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