# Math Help - Finding Interval of Convergence

1. ## Finding Interval of Convergence

Can anyone help me solve this?

My friend's got 17.

Im confused.

2. ## Re: Finding Interval of Convergence

Originally Posted by weijing85
Can anyone help me solve this?

My friend's got 17.

Im confused.

The series

$\frac{1}{1+z}=1-z+z^2-z^3+z^5-z^5+...$

is convergent if and only if $|z|<1$.

In your case, $z=\frac{x-12}{5}$, so $|x-12|<5$. If $x\geq 12$, then you get $x-12<5 \implies x<17$. If $x\leq 12$, you get $-x+12<5 \implies x> 7$. Thus your interval of convergence is $(7,17)$