SOLUTION: a. write 0.75 as an infinite geometric series. (bar is over 75) b. express 0.75 as a fraction in lowest terms by finding the sum of the series. (bar is over 75)

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Question 81942This question is from textbook
: a. write 0.75 as an infinite geometric series. (bar is over 75)

b. express 0.75 as a fraction in lowest terms by finding the sum of the series.
(bar is over 75)This question is from textbook

Found 2 solutions by checkley75, jim_thompson5910:
Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
25/33=.75757575757575757575757575757575

Answer by jim_thompson5910(21685) (Show Source):
You can put this solution on YOUR website!
Since the decimal repeats, we can break up the series as

0.75+0.0075+0.000075...

So this represents a sequence. Notice the first term is 0.75, so . The common ratio (the constant factor) is then simply

So altogether we have the sequence

or

Notice if n=0 we get our first term 0.75, if n=1, we get 0.0075 etc.

So the series is simply: