write 0.12......( repaeting decimal) as a geometric sequence?
is this right?
11/90
thanks!
Nope.
Use a calculator.
11/90 = .122222222
Try 11/99.
Sorry, try 12/99
To write the repeating decimal 0.12...(repeating decimal) as a geometric sequence, we can think of it as the sum of an infinite geometric series.
Let's call the repeating decimal x. We can express x as the sum of the following series:
x = 0.12... = 0.121212... = 0.12(1/100 + 1/10000 + 1/1000000 + ...)
To express this as a geometric sequence, we need to find the common ratio. The common ratio, r, is obtained by dividing the second term by the first term.
In this case, the first term is 1/100 and the second term is 1/10000. Therefore:
r = (1/10000) / (1/100) = 1/10000 * 100 = 1/1000000
So, the geometric sequence representation of 0.12...(repeating decimal) is:
0.12...(repeating decimal) = 1/100 + (1/100)(1/1000000) + (1/100)(1/1000000)(1/1000000) + ...
By simplifying the terms, we get:
0.12...(repeating decimal) = (1/100) + (1/100)^2 + (1/100)^3 + ...
Unfortunately, the exact value of the sum of this series cannot be determined, as it is an infinite geometric series. However, we can approximate it using the formula for the sum of an infinite geometric series:
S = a / (1 - r)
where S is the sum of the series, a is the first term, and r is the common ratio.
In this case, a = 1/100 and r = 1/10000. Substituting these values into the formula, we get:
S = (1/100) / (1 - 1/10000)
Simplifying, we find:
S = (1/100) / (9999/10000) = 1/9999
So, the approximate value of the sum of the geometric sequence representing 0.12...(repeating decimal) is 1/9999.
Therefore, the answer is not 11/90 or 12/99.