# Student the power serie

• Jan 2nd 2010, 10:03 AM
dhiab
Student the power serie
1)Student the power serie :

$\sum n^{(-1)^{n}}\times x^{n}$

in : $x = 1,x = \frac{1}{2}
$

2) Same question but :

$\left\{ \begin{array}{l}
x = a \\
\left| a \right| < 1 \\
\end{array} \right.
$

Give the radius and int of convergence
• Jan 3rd 2010, 10:22 PM
Dark Sun
Since the $\lim _{n\rightarrow \infty }\limits n^{(-1)^n}\times x^n\neq 0$, we cannot conclude that the series converges.