Recent content by Tommy941

Ahh Mark44 I see what you mean, so if I can show z_n is decreasing using the ratio test, then I can say it converges to 0 (as the sequence is clearly bounded below by 0). I was also thinking could I do this by writing the denominator in polar form, rationalising it, then splitting the sequence...

Ray Vickson - I meant literally does the sequence z_n converge

Thanks guys, Mark44 - I don't think I can use the ratio test because it is a test for if series converge. pasmith - I have never seen that method before :/ What if i split the sequence into its real and imaginary parts then show that each of those converge which will imply the sequence converges?

Homework Statement Determine whether the sequence zn = n/((1+i)n) converges and rigorously justify your answer. Homework EquationsThe Attempt at a Solution I have attempted an ε-n proof using my limit as 0 (as exponentials grow faster than polynomials I assumed this was the correct limit)...

Thanks HallsofIvyy I think I will be able to do it now. Is it O.K for me to say that for suitably large n, |an-2|<ε<1 ⇒ |an+2|<3 so 3 can be considered an upper bound on an when n is suitably large??

Homework Statement Let an → 2. Prove from first principles (i.e. give a direct ε-N proof) that an2 → 4. Homework EquationsThe Attempt at a Solution I have tried considering |an-2|2 and considering that |an2-4| = |(an+2)(an-2)| but I could not get either of these methods to work. Would someone...