## 8367 #45

Forum for the GRE subject test in mathematics.
breezeintopl
Posts: 16
Joined: Sun Jul 19, 2009 12:29 pm

### 8367 #45

#45
why is \infty but not 1/e?

thank you~~~

joey
Posts: 32
Joined: Fri Oct 16, 2009 3:53 pm

### Re: 8367 #45

Did you mean 8767?

Use the ratio test. We get
$$\left| \frac{a_{n+1}}{a_n}\right| = \frac{e|x|}{n+1} \to 0.$$

Hence, the series is absolutely convergent, regardless of x.

What's your reason for picking 1/e?

breezeintopl
Posts: 16
Joined: Sun Jul 19, 2009 12:29 pm

### Re: 8367 #45

joey wrote:Did you mean 8767?

Use the ratio test. We get
$$\left| \frac{a_{n+1}}{a_n}\right| = \frac{e|x|}{n+1} \to 0.$$

Hence, the series is absolutely convergent, regardless of x.

What's your reason for picking 1/e?
oh~~3Q~~I just forget the ratio test,whether is n-->\infty or for all n=0,1,2.... So I make a mistake...

thx~~