find the convergent set of the power series.
heres the equation for problem2: http://img297.imageshack.us/img297/6606/untitledoy2.jpg
find the convergent set of the power series.
heres the equation for problem2: http://img297.imageshack.us/img297/6606/untitledoy2.jpg
Use the ratio test,
$\displaystyle \frac{n+2}{n+1}\to 1$
Thus, the radius of convergence is the reciprocal of that, namely, 1.
Thus,
$\displaystyle |x|<1$
Is absolute convergence.
Check endpoints $\displaystyle x=\pm 1$.
For $\displaystyle x=1$ have an incomplete harmonic series thus it diverges.
And for $\displaystyle x=-1$ we have an incomplete alterning harmonic thus it converges.
$\displaystyle [-1,1)$
Is the interval of convergence.