Determine the sum of the following geometric series 1/32 + 1/16 + … + 256

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The geometric series consists of the following terms, 1/32, 1/16, ... 256

The first term is a = 1/32.

From the first two terms the common ratio is r = `(1/16)/(1/32) = 2`

The nth term of a geometric series is `a*r^(n - 1)`

`256 = (1/32)*2^(n - 1)`

=> `2^(n - 1) = 256*32 = 2^13`

=> n = 14

The sum of the first 14 terms of the series is `(1/32)*(2^14 - 1)/(2 - 1) = 511.96875`

**The sum of **`1/32 + 1/16 + … + 256 = 511.96875`

The geometric series consists of the following terms, 1/32, 1/16, ... 256

The first term is a = 1/32.

From the first two terms the common ratio is r =

The nth term of a geometric series is

=>

=> n = 14

The sum of the first 14 terms of the series is

**The sum of **

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