Bah. Where did the -1 come from?

[physicsnoob93]

http://img48.imageshack.us/img48/6110/qnisstb4.jpg

I always get the positive and negatives confused. I don't have a teacher to guide me so help would be appreciated. The correct answer is in green ink.

Thanks

 

[HallsofIvy]

At one point you have converted 1/(x+2) into (-1)/(2- x). That's wrong. That would be equal to 1/(x-2) not 1/(x+ 2). What you want, rather, is 1/(x+ 2)= 1/(2+x)= 1/(2-(-x)). Then dividing by numerator and denominator by 2: (1/2)/(1-(-x/2)). The "r" in your geometric series is -x/2, not x/2.