Recent content by MelanieSwan

Could you explain more about this? I don't get the part from L-M < 2e >> L-M<=0 . Thanks very much for replying :)

Homework Statement true or false. prove or give counter example: 1. with x approaches to infinity suppose that lim f(x) = L and lim g(x) = M and f(x)< g(x), then L< M. 2. with x approaches to infinity suppose that lim f(x) = L and lim g(x) = M and f(x)<= g(x), then L<=M for all x in D...

I am doing my homework and somehow again I couldn't work out this problem. Any help would be much appreciated: 1. Homework Statement Consider the sequences {an} and {bn} where sequence {an} diverges to infinity and the sequence {anbn} converges. Prove that {bn} must converge to zero 2...

I got it. thanks very much. :)

sorry I have been away and didn't have the chance to check this thread out. Yes, you're right. I'm confused about that. So that means when n=1, 3n/(n-1) is not defined so we cannot use this sequence as a counter example? Could you give me some hint on how to work out this problem?

this is what I am confused about. Obviously 3n/(n-1) converges at 3, but is it right to say that it converges with n=1 to n=infinity? I think it's must be that 3n/(n-1) converges at 3 with n=2 to n= infinity? :S

ok i thought about that but how can I put n=1 to n=infinity into work using this?

Thank you all very much. As you my guess I started learning about sequences and haven't got used to them yet. One of the questions I raised during the lecture was that if a sequence {an} converges with n=2 to n=infinity, does it converge with n=1 to n=infinity. Obviously it may not since look...

so it should be: an = 7(-1)^n ^^

Oh thanks very much. I think I misunderstand the question as "with all values of n". That's why i got stuck. Thanks for your answers :)

Homework Statement Give an example of a sequence {an} whose value is 7 for infinitely many values of n, but which does not converge to 7 Homework Equations The Attempt at a Solution I tried to think about such a sequence but cannot come up with any that satisfies that its value...