Repeating Decimals As An Infinite Series
Repeating decimals can also be expressed as an infinite series. That is, repeating decimals can be shown to be a sum of a sequence of numbers. To take the simplest example,
The above series is a geometric series with the first term as 1/10 and the common factor 1/10. Because the absolute value of the common factor is less than 1, we can say that the geometric series converges and find the exact value in the form of a fraction by using the following formula where a is the first term of the series and r is the common factor.
Read more about this topic: Repeating Decimal
Famous quotes containing the words repeating, infinite and/or series:
“We can best help you to prevent war not by repeating your words and following your methods but by finding new words and creating new methods.”
—Virginia Woolf (1882–1941)
“In the order of literature, as in others, there is no act that is not the coronation of an infinite series of causes and the source of an infinite series of effects.”
—Jorge Luis Borges (1899–1986)
“The professional celebrity, male and female, is the crowning result of the star system of a society that makes a fetish of competition. In America, this system is carried to the point where a man who can knock a small white ball into a series of holes in the ground with more efficiency than anyone else thereby gains social access to the President of the United States.”
—C. Wright Mills (1916–1962)