# Thread: interval of convergence of a power series

1. ## interval of convergence of a power series

need help figuring out what R is for the following power series...

summation from 0 to infinity {[(1+5^n)/n!]x^n]}

2. Remember that: $e^x=1+x+\frac{1}{2!}\cdot{x^2}+\frac{1}{3!}\cdot{x ^3}+...$ for all real $x$

You can even calculate your sum considering the identity above .

3. i didnt get how u changed the whole numerator of the summation to sin(k).. it was 1+5^n, n! ... where did 1+5^n go?

4. Originally Posted by PaulRS
Remember that: $e^x=1+x+\frac{1}{2!}\cdot{x^2}+\frac{1}{3!}\cdot{x ^3}+...$ for all real $x$
What do you think that as to do with it posted series?
I dare say nothing!

Originally Posted by ramzouzy
need help figuring out what R is for the following power series...
summation from 0 to infinity {[(1+5^n)/n!]x^n]}
Have you used either the ratio or the root test?

5. I suggested:

$e^x+e^{5\cdot{x}}=\sum_{n=0}^{\infty}{\left(\frac{ 1+5^n}{n!}\right)}\cdot{x^n}$ for all real $x$ which is the series you wanted

I do not see sin (n) there

But if you want to do it by the root test you just have to remember that $\lim_{n\rightarrow{+\infty}}\frac{\sqrt[n]{n!}}{\frac{n}{e}}=1$