#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
$$\left| \frac{a_{n+1}}{a_n}\right| = \frac{e|x|}{n+1} \to 0.$$
Hence, the series is absolutely convergent, regardless of x.
What's your reason for picking 1/e?
Use the ratio test. We get
$$\left| \frac{a_{n+1}}{a_n}\right| = \frac{e|x|}{n+1} \to 0.$$
Hence, the series is absolutely convergent, regardless of x.
What's your reason for picking 1/e?
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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
$$\left| \frac{a_{n+1}}{a_n}\right| = \frac{e|x|}{n+1} \to 0.$$
Hence, the series is absolutely convergent, regardless of x.
What's your reason for picking 1/e?
thx~~