I'm a newbie so didn't really know where to post this, but I hope someone here can help me!I'm just beginning to study sequences, and I'm getting nowhere with it. Can anyone please help me with these two problems:
1.)Show that the sequence (1/n^k)nEN is convergent if and only if k>=0, and that the limit is 0 for all k>0.
2.)Determine the least value of N such that n/(n^2+1)<0.0001 for all n>=N
On part 2 though, why is it ?and not ?
It is. It is just easier to solve the equality to get n=9999.9999 but since n needs to be a natural number we choose 10,000.
Originally Posted by simplysparklers
P.S we don't use the other root. (why?)
I hope this helps.
It does help, thank you so much! :)
I do have to ask though, why isn't the other root used??
& in the first question, ok, I get the first part, and taking the diferent values for k, and I understand in my head because it is bounded below by 0, it must converge to 0, but I don't get the proof? Like, what do I do with
Hint: let http://www.mathhelpforum.com/math-he...fcabafdf-1.gif Choose http://www.mathhelpforum.com/math-he...69506a61-1.gif ?Sorry about this, but could you spell it out for me please?I'm never hit such a absolute immovable wall before over a maths topic, but I am not getting sequences at all (Sadsmile) and I have this assignment due in soon (Worried) Thank you so much for your time and help! (Handshake)
Thank you so much!I get all of the first one now! (Sun)
Originally Posted by TheEmptySet
The thing I still don't get about the 2nd one,(& I'm sorry to keep bothering you on this!), is that normally you have n> [some equation with epsilon], but in his case you are just given the value of epislon, so you don't have to sub a value for epsilon into an equation to get the value of N...so where do you get the value of N?How does having n=10,000 help?
And a follow up question, you know the way it should be |a_n-L|< epsilon whenever n > N, well what if the sign is reversed?And it's |a_n-L|>= epislon for all n > N? It's in a similar question to the above one, i.e.:
Determine the least value of N such that n^2 + 2n >= 9999 for all n>N
Thank you so much for all you help!I'm stumped!
It certainly does TheEmptySet!!Thank you so so much for your help!!You rock!!! (Rock)