SOLUTION: 75+15+3+... Find the sum, if it exists. Help? how to solve?

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Question 607406: 75+15+3+...
Find the sum, if it exists.
Help? how to solve?

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
75+15+3+...
To show that this is a geometric series, and to find r,  
we divide the 2nd term by the 1st term.  Then we divide 
the 3rd term by the 2nd term, and if those two numbers
are the same then it is a geometric series and r = what
we got when we divided those.

15÷75 = 15%2F75 = 1%2F5

3÷15 = 3%2F15 = 1%2F5

They are the same so it is a geometric series with r = 1%2F5.

It is an infinite series with sum given by the formula

S%5Binfinity%5D = a%5B1%5D%2F%281-r%29 = 75%2F%281-1%2F5%29 = 75%2F%284%2F5%29 = 75÷4%2F5 = 75×5%2F4 = 375%2F4 = 93.75

Edwin