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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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):
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
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.
