"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.
––––– = 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?
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