Can you show us what you tried please?
"using the definition (epsilon-N definition), show that the sequences (-1)^n(1/3n) + (1/2n) and cos(n^2)/(3n+1) both converge to the limit zero". ok, so i know the limit and i know the process. i can handle these questions ok when it is just a polynomial sequence but, for example, what do i do with the (-1)^n? the first step i need to do is deal with this and i don't know how to proceed. similar for cosines.
as i said, i encountered a problem with the first step. if someone can tell me how to deal with the (-1)^n, i can do the rest. but i cant try anything beyond that because the obstacle i need help with is right at the beginning..
hmmm its 1/3n, not (1/3)^n. so does this make a difference? my thought was that i should just say that the whole thing is less than (something?) regardless of sign so i.e. take the value for even n and say its less than that?
what i did is:
etc.... is this the same/an ok way of expressing it? basically saying that 'it has to be less than what it is if n is even', as that gives the highest absolute value. i mean its technically true, do i have to be more rigid in the conditions here? it leads to same the resut. and yes i am confortable with the rest of the proof it was just how to deal with the (-1)^n i have never come across. basically the differnce is i put the two parts over a common denomnator instead of splitting. in fact once the (-1)^n is gone i can just get rid of the modulus altogether since its all always positive then.