SOLUTION: Can you help me please? I will appreciate your answer. Exercise: The sum of the infinite geometric series (x-1)+(x-1)^2+(x-1)^3+ ... is 1/3. Determine the Value of "x". Th

Algebra ->  Sequences-and-series -> SOLUTION: Can you help me please? I will appreciate your answer. Exercise: The sum of the infinite geometric series (x-1)+(x-1)^2+(x-1)^3+ ... is 1/3. Determine the Value of "x". Th      Log On


   

Question 352077: Can you help me please?
I will appreciate your answer.
Exercise:
The sum of the infinite geometric series
(x-1)+(x-1)^2+(x-1)^3+ ... is 1/3. Determine the Value of "x".
Thank You!
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
>Let S=(x-1)+(x-1)^2+(x-1)^3+ ...,

if we add 1 to S and multiply by (x-1) we get the same series : hence we have (S+1)*(x-1) equals S again : S=(x-1)*(S+1) => S(1-(x-1))=x-1

=> S=(x-1)/(2-x)

here S=1/3, hence (x-1)/(2-x)=1/3 => 3x-3=2-x => 4x=5 => x=5/4

Verification : (x-1)*(S+1)=1/4*(1+1/3)=1/4*4/3=1/3=S