Sum to Infinity of a Geometric Series

[odolwa99]

Homework Statement

Q. Find, in terms of x, the sum to infinity of the series...

1 + (\frac{2x}{x + 1}) + (\frac{2x}{x + 1})^2 + ...

Homework Equations

S\infty = \frac{a}{1 - r}

The Attempt at a Solution

S\infty = \frac{a}{1 - r}

a = 1

r = U2/ U1 = (\frac{2x}{x + 1})/ 1 = \frac{2x}{x + 1}

\frac{1}{1 - (2x/ x + 1)}

\frac{x + 1}{1 - 2x}

Ans.: From textbook: \frac{x + 1}{1 - x}

Can anyone help me figure out where the 2x becomes just x? Thank you.

 

[rock.freak667]

If you take

\frac{1}{x-\frac{2x}{x+1}} \times \frac{x+1}{x+1}

you will get

\frac{x+1}{1(x+1)-2x}

Which simplifies to the answer you want.

 

[odolwa99]

Thanks for clearing that up. I appreciate the help.