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Find the sum of the infinite geometric sequence that begins 1/12, 1/18, 1/27, …

Sagot :

sqdancefan

Answer:

  1/4

Step-by-step explanation:

The sum of an infinite geometric series is given by the formula ...

  S = a/(1 -r)

where 'a' is the first term, and r is the common ratio.

Application

Here, the first term is 1/12, and the common ratio is ...

  (1/18)/(1/12) = 12/18 = 2/3

Then the sum is ...

  S = (1/12)/(1 -2/3) = (1/12)/(1/3) = 3/12 = 1/4

The sum of the infinite series is 1/4.

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