Posted by **lili** on Monday, April 12, 2010 at 2:10am.

express the given repeating decimal

0.159159159 as a fraction

- sequence and series -
**Damon**, Monday, April 12, 2010 at 5:00am
n = 0.159159159...

three numbers 159 repeat

so multiply by 10^3 = 1000

1000n =159.159159159 now subtract n

n = .159159159

-------------------------------

999n = 159.000000....

so

n = 159/999

- sequence and series -
**Damon**, Monday, April 12, 2010 at 5:29am
or

159*10^-3 + 159*10^-6 +159*10^-9 ....

each term is 10^-3 times previous

sum of infinite geometric series with first term g and ratio r

S = g/(1-r)

here g = .159

and r = .001

so

S = .159/(1-.001) = .159/.999 =159/999

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