Can someone please help me to compute the radius of convergence of
$$1 + \frac {x^1} {1} + \frac {x^2} {2} + \frac {x^3} {3} + \dots ?$$
Asked
Active
Viewed 70 times
-1
-
I have tried to correct your MathJax formatting, please check whether my edit has preserved the intended meaning. – Alex M. Oct 14 '16 at 15:53
-
Yes Alax you are right I am new on this site can you please tell me how you corrected it so I will not do this mistake again – user378334 Oct 14 '16 at 15:55
-
The history of edits is available by clicking on the "edited ... ago" link. – hardmath Oct 14 '16 at 19:25
2 Answers
0
Hint: $R=\lim_{n \to \infty} \left|\frac{a_n}{a_{n+1}}\right|=\lim_{n \to \infty} \left|\frac{1/n}{1/(n+1)}\right|=\lim_{n \to \infty} \left|\frac{n+1}{n}\right|=1$
MrYouMath
- 15,833
0
your series is $\sum a_n x^n$
with $a_n=\frac{1}{n}>0$
$\lim_{n \to +\infty} \frac{a_{n+1}}{a_n}=$
1.
which is the inverse of convergence radius.
your radius is $1$
hamam_Abdallah
- 62,951
-
What happens if the sign of series alters for this that is first term is positive, second term negative and so on – user378334 Oct 14 '16 at 16:02
-
you compute limit of $|\frac{a_{n+1}}{a_n}|$ to obtain the inverse if $R$. – hamam_Abdallah Oct 14 '16 at 16:04