#45
why is \infty but not 1/e?
thank you~~~
8367 #45
Re: 8367 #45
Did you mean 8767?
Use the ratio test. We get
$$\left \frac{a_{n+1}}{a_n}\right = \frac{ex}{n+1} \to 0.$$
Hence, the series is absolutely convergent, regardless of x.
What's your reason for picking 1/e?
Use the ratio test. We get
$$\left \frac{a_{n+1}}{a_n}\right = \frac{ex}{n+1} \to 0.$$
Hence, the series is absolutely convergent, regardless of x.
What's your reason for picking 1/e?

 Posts: 16
 Joined: Sun Jul 19, 2009 12:29 pm
Re: 8367 #45
oh~~3Q~~I just forget the ratio test,whether is n>\infty or for all n=0,1,2.... So I make a mistake...joey wrote:Did you mean 8767?
Use the ratio test. We get
$$\left \frac{a_{n+1}}{a_n}\right = \frac{ex}{n+1} \to 0.$$
Hence, the series is absolutely convergent, regardless of x.
What's your reason for picking 1/e?
thx~~