SOLUTION: Please help me with this problem: Resolve into infinite series {{{ax/(a-x)}}} I can't show how I tried on this problem because it is very complicated! I did try several times t

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Question 1116740: Please help me with this problem: Resolve into infinite series
I can't show how I tried on this problem because it is very complicated! I did try several times though.
This is the answer from my key book: x+x^2/a+x^3/a+x^4/a,ect., to infinity
I don't understand how the fractions are able to keep repeating. When I worked the problem I got as far as x+x^2/a, but no farther.
I appreciate any help you can offer!
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

It's done by special long division:

       x + x²/a + x³/a² + ∙∙∙ 
a - x)ax
      ax - x²
           x²   - x³/a²
                  x³/a² -    

If you need further explanation, just ask in the note-form
below and I'll get back to you by email.

Edwin
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

            The formula in your post is written   I N C O R R E C T L Y.

            The correct formula is   T H I S:

             = + + + +  .  .  .  ,   ect.,   to infinity.

.
It is not difficult to prove it   //   if you know the formula for the sum of an infinite geometric series . . . 

 =  = .


The very right fraction    is the sum of an infinite geometric progression with the first term of "1" and the common ratio of :


 =  1 +  +  +  + . . .      (1)


Now multiply both sides of (1) by x, and you will get the required solution


 = x +  +  +  + . . .


QED.

Solved.



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