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avatar+59 

10 + 10r + 10r^2 + 10r^3 + 10r^4 + ... = 8 

 Aug 6, 2023
 #3
avatar+701 
+3

"The formula for the sum of an infinite series is a/(1-r), where a is the first term in the series and r is the common ratio i.e. the number that each term is multiplied by to get the next term in the sequence. To find r, divide any term in the series by the prior term."  

 

I didn't know that, I just copied it off the internet.  Let's see if I can use it right.    

 

Considering  10 + 10r + 10r^2 + 10r^3 + 10r^4 + ... = 8    

 

                      The first term is 10 and it looks like r is r. 

 

So       

                                        10      

                                      –––––  =  8   

                                       1 –  r    

 

                                            10  =  8 – 8r   

 

                                             8r  =  8 – 10   

 

                                               r  =  –0.25   

 

Can it really be that easy?  Would somebody who knows how      

to solve this kind of problem please check these figures?                      

.

 Aug 7, 2023
 #6
avatar+59 
0

thank you!

dumplings  Aug 7, 2023
 #4
avatar+126971 
+6

We have a geometric series  where the  ratio between successive terms  =  r

 

The sum of such a series, S, can be represented by

 

S =   first term / ( 1 - r)   .....so we have.......  

 

8 =10 / (1 - r)

 

1 - r = 10/8

 

r = 1 - 10/8

 

r =  -2/8  =  -1/4

 

cool cool cool

 Aug 7, 2023
 #5
avatar+59 
+1

thank you!

dumplings  Aug 7, 2023
 #7
avatar+701 
+3

 

Thank you.  I tried to give the answer a heart, but it wouldn't add one.  

.

Bosco  Aug 7, 2023

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