Thread: Power Series

-qbkr21

You use the ratio test improperly,

$\displaystyle \left| \frac{(-1)^{n+1}(x+3)^{n+1}}{(n+1)5^{n+1}} \cdot \frac{n5^n}{(-1)^n(x+3)^n} \right| \to \frac{|x+3|}{5}$

We need that,
$\displaystyle \frac{|x+3|}{5} < 1$

Solve from there thyself.