Find the interval of convergence of $$\sum_{1}^{\infty} \frac{ 8x^n }{ n }$$

I am not sure what I am doing wrong here, I'm pretty sure this should be the interval [-1/8,1/8) but that seems to be wrong.

Question

Find the interval of convergence of $$\sum_{1}^{\infty} \frac{ 8x^n }{ n }$$

I am not sure what I am doing wrong here, I'm pretty sure this should be the interval [-1/8,1/8) but that seems to be wrong.

anonymous · Answer

I have |x|<1/8 when I solve this, but apparently that isnt correct, unless my brackets are off.

anonymous · Answer

you are getting confused by the $8$ ignore it

anonymous · Answer

$$\sum_{n=1}^{\infty} \frac{ 8x^n }{ n }=8\sum_{n=1}^{\infty} \frac{ x^n }{ n }$$

anonymous · Answer

it is a constant, it is not being raised to the power of $n$ so just pull it out front, it does not effect the interval of convergence

anonymous · Answer

ah crap, thanks, thats a silly mistake.

anonymous · Answer

(-1,1) with open brackets then

anonymous · Answer

no, i think you are good at $-1$

anonymous · Answer

i.e. 
$$[-1,1)$$

anonymous · Answer

ah right I see that, -1 is fine as it would end as - (-1). THanks for the help!

anonymous · Answer

yw