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:
“The echo is, to some extent, an original sound, and therein is the magic and charm of it. It is not merely a repetition of what was worth repeating in the bell, but partly the voice of the wood; the same trivial words and notes sung by a wood-nymph.”
—Henry David Thoreau (1817–1862)
“This moment exhibits infinite space, but there is a space also wherein all moments are infinitely exhibited, and the everlasting duration of infinite space is another region and room of joys.”
—Thomas Traherne (1636–1674)
“Depression moods lead, almost invariably, to accidents. But, when they occur, our mood changes again, since the accident shows we can draw the world in our wake, and that we still retain some degree of power even when our spirits are low. A series of accidents creates a positively light-hearted state, out of consideration for this strange power.”
—Jean Baudrillard (b. 1929)