Hey folks!
I have been super busy of late. I shall write more on my graduate school experience (as a neophyte) later in a separate post during fall break. In the mean time, I have an interesting problem to share with you:
To all readers with single-variable calculus background (US Calculus II equivalent; UMICH Math 116 equivalent; UNC Math 232 equivalent): Determine whether the following sequence converges or diverges. Justify your answer.
I shall reveal the answer in a week or so. Happy attempting!
Ugh… math… calculus summore!!! I’ll pass.
Doesn’t it converge to zero?
remember there are different ways (tests) to see if it converges or diverges…ahah, but too bad i’ve returned what i’ve learned to my lecturer. :p
Enjoy your fall break in Chicago. Send my regards to Vivian, she’s been missing in action for such a long time… force her to update us on mm-daily!!! =)
Yeah, I think it does. Sorry if I’m wrong, been awhile since I was in any math class. Graduated. Who knows, one day I may go back to school and get a terrible itch scratched. Learning more math, yeah!
a_(n) = -3^(n)/n!
a_(n+1) = -3^(n+1)/(n+1)!
So, a_(n+1)/a_n(n) …
-3^(n) * -3 * n! / [ -3^(n) * (n+1)n!]
So, after some cancelling =>
-3 / (n+1)
Take the limit of the absolute value as n approaches infinity, gives you 1/infinity, which converges to 0.
Yeah. Holy shit. I still remember this.
SO what is the point of this exercise? Aren’t you in grad school. Shouldn’t you know this?
Eeer beyondyonder, did Eric at any point say he didn’t know it? This is not a blog for math students, so the point of this question is to share what Eric thinks might be of interest to his readers.
hmmm no, I guess not.
Yeah, I’m sure he knows. It’s great that he does this for math students…
Don’t attack me yo. I think what he is doing is great.
I made the comment just because I want to post another comment but I didn’t have anything else to say, so I just typed the first thing that was on my mind. I suppose if I didn’t have anything to say then I should have just shut up…
All, let’s end this slightly tempestuous exchange of comments, shall we?
Chang Yang, I appreciate your standing up for me. Thank you! And Beyondonder, I initially perceived your words as some sort of personal attacks, too. But thanks for clarifying your intentions.
The ratio test is a good idea, but it’s for series, not sequences.
The solution has been posted in a separate post, ahead of my one week deadline!
Initially I thought this would be solved by a geometric convergence test… until I realized that the factorial on the denominator means it would increase exponentially faster than the numerator. So the series converges to zero while alternating between (+)ve and (-)ve signs.