# find convergent set of the power series

• January 31st 2007, 07:38 AM
rcmango
find convergent set of the power series
find the convergent set of the power series.

heres the equation for problem2: http://img297.imageshack.us/img297/6606/untitledoy2.jpg
• January 31st 2007, 09:45 AM
ThePerfectHacker
Use the ratio test,
$\frac{n+2}{n+1}\to 1$
Thus, the radius of convergence is the reciprocal of that, namely, 1.
Thus,
$|x|<1$
Is absolute convergence.
Check endpoints $x=\pm 1$.
For $x=1$ have an incomplete harmonic series thus it diverges.
And for $x=-1$ we have an incomplete alterning harmonic thus it converges.
$[-1,1)$
Is the interval of convergence.
• January 31st 2007, 04:06 PM
rcmango
thankyou.