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The formula for the sum of an infinite geometric series, s=a1/1-r, may be used to convert 0.23 to a fraction. What are the values of a1 and r?

Respuesta :

Edufirst
I believe the number to be converted to a fraction is 0.232323..., this is 0.23 periodic.

The fomula is right:

 [tex]S= \frac{ a_{1} }{1-r} [/tex]

Where [tex] a_{1} [/tex]  is 0.23 and r is 1/100

Check it here:

    23/100          23/100         23
-------------- =    ----------- =   ------- = 0.232323...
1 - 1/100          99/100          99

So, the answer is   [tex] a_{1}= [/tex]   23/100 and r = 1/100

The value of [tex]a_1[/tex] is 0.23 and the value of r is 1/100 and this can be determined by using the concept of geometric progression.

Given :

  • The formula for the sum of an infinite geometric series, [tex]s = a_1/(1-r)[/tex].
  • Fraction -- 0.23 (Repeated)

The following steps can be used in order to determine the values of [tex]a_1[/tex] and r:

  • Step 1 - The given repeated fraction can be written as:

                     0.2323232323... = 0.23 + 0.0023 + 0.000023 +...

  • Step 2 - The above series is in geometric progression.

  • Step 3 - So, the value of [tex]a_1[/tex] is 0.23.

  • Step 4 - The value of the geometric ratio can be calculated as:

                  [tex]r = \dfrac{0.0023}{0.23}[/tex]

                 [tex]r = \dfrac{1}{100}[/tex]

The value of [tex]a_1[/tex] is 0.23 and the value of r is 1/100.

For more information, refer to the link given below:

https://brainly.com/question/14320920

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