Thread: Quick Power Series Question

the series is..

[(3^n)(x+4)^n]/(n^0.5)

did the ratio, ended up with

3(x+4)(n^.5)/(n+1)^.5

I got the interval of convergence correctly, but for the radius, the back of the book is saying 1/3 (when, what I'm having right now is 3x+12<1 ).

So my question is just.. how did they get the 1/3? Do numbers not count if they're not attached to variables or did I just make a mistake

Originally Posted by coolguy99

the series is..

[(3^n)(x+4)^n]/(n^0.5)

did the ratio, ended up with

3(x+4)(n^.5)/(n+1)^.5

I got the interval of convergence correctly, but for the radius, the back of the book is saying 1/3 (when, what I'm having right now is 3x+12<1 ).

So my question is just.. how did they get the 1/3? Do numbers not count if they're not attached to variables or did I just make a mistake

You did a great job. Think of radius as the maximum distance away from x. To help see this consider the following calculations.
First of all the ratio test gives us,







So you can see x can move 1/3 units in either direction from -4.

An alternate way of seeing this is from the ratio test you have

(this is the way you'd do it on a test {quicker}).

If you cannot see it by this form, then let's go one more step