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odolwa99
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Homework Statement
Q. Find, in terms of x, the sum to infinity of the series...
1 + [itex](\frac{2x}{x + 1})[/itex] + [itex](\frac{2x}{x + 1})^2[/itex] + ...
Homework Equations
S[itex]\infty[/itex] = [itex]\frac{a}{1 - r}[/itex]
The Attempt at a Solution
S[itex]\infty[/itex] = [itex]\frac{a}{1 - r}[/itex]
a = 1
r = U2/ U1 = [itex](\frac{2x}{x + 1})[/itex]/ 1 = [itex]\frac{2x}{x + 1}[/itex]
[itex]\frac{1}{1 - (2x/ x + 1)}[/itex]
[itex]\frac{x + 1}{1 - 2x}[/itex]
Ans.: From textbook: [itex]\frac{x + 1}{1 - x}[/itex]
Can anyone help me figure out where the 2x becomes just x? Thank you.