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8367 #45

Posted: Thu Nov 05, 2009 9:14 pm
by breezeintopl
#45
why is \infty but not 1/e?

thank you~~~

Re: 8367 #45

Posted: Thu Nov 05, 2009 11:15 pm
by joey
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?

Re: 8367 #45

Posted: Fri Nov 06, 2009 12:47 am
by breezeintopl
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~~