The formula for the sum of an infinite geometric series, cap s is equal to the fraction with numerator A sub 1 and denominator 1 minus r , may be used to convert line segment 0 point 2 3 to a fraction. What are the values of A sub 1 and r ?
Answer
A
A sub 1 is equal to 23 comma r is equal to 1 over 100
B
A sub 1 is equal to 23 tenths comma r is equal to 1 tenth
C
A sub 1 is equal to 23 over 100 comma r is equal to 1 over 100
D
A sub 1 is equal to 23 over 100 comma r is equal to 100
Explanation
The repeating decimal 0.232323… can be written as 0.23 + 0.0023 + 0.000023 + … . The first term is A₁ = 23/100, and each term is 1/100 of the previous term, so r = 1/100. Therefore, choice D gives the correct values.
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