Question

b) Determine the radius of convergence and the convergence interval (with analysis of the endpoints) for the power series
\(\Large \sum_{n=0}^{\infty} \frac{x^{n}}{2^{(n^{2})}}\)

Answer 1

\[
\frac{x^{n+1}}{\frac{2^{(n+1)^
2}
x^n}{2^{n^2}}}=\frac{x}{2^{
2 n+1}}
\]

Answer 2

So R =Infinity

Answer 3

\[
\lim_{n\to \infty} \frac{x^{n+1}}{\frac{2^{(n+1)^
2}
x^n}{2^{n^2}}}=\lim_{n\to \infty}\frac{x}{2^{
2 n+1}}=0
\]
for any x.

Answer 4

is it our end solution mr Elias, i need to give my last homework tomorrow and need at least 6 points :)

Answer 5

?

Answer 6

Yes

Answer 7

ok thank you very much :)

Answer 8

yw