Can anyone help me solve this?
My answer is 5.
My friend's got 17.
Im confused.
The series
$\displaystyle \frac{1}{1+z}=1-z+z^2-z^3+z^5-z^5+...$
is convergent if and only if $\displaystyle |z|<1$.
In your case, $\displaystyle z=\frac{x-12}{5}$, so $\displaystyle |x-12|<5$. If $\displaystyle x\geq 12$, then you get $\displaystyle x-12<5 \implies x<17$. If $\displaystyle x\leq 12$, you get $\displaystyle -x+12<5 \implies x> 7$. Thus your interval of convergence is $\displaystyle (7,17)$
So your friend is correct.