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)

Algebra ->  Sequences-and-series -> 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)      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
25/33=.75757575757575757575757575757575

Answer by jim_thompson5910(35256) About Me  (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 a%5B1%5D=0.75. The common ratio (the constant factor) is then simply

r=0.0075%2F0.75=1%2F100

So altogether we have the sequence

a%5Bn%5D=0.75%281%2F100%29%5En or a%5Bn%5D=%283%2F4%29%281%2F100%29%5En

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

So the series is simply:

sum%28+%283%2F4%29%281%2F100%29%5Ei%2C+i=0%2C+infinity+%29