does this sequence converge or diverge?

Question

anonymous · Answer

please help me

anonymous · Answer

$$\frac{ 2n+(-1)^n*5 }{ 4n-(-1)^n*3}$$

anonymous · Answer

i would say it converges to $\frac{1}{2}$

anonymous · Answer

that $\pm3$ and $\pm5$ stuff out at the end really has no effect 
think about what you would get if say $n=1,000,000$

anonymous · Answer

yes i found that it converges to 1/2 as well. in this case the (-1)^n*5 part would be a constant, so in the future just for curiosity do all monomials dominate constants when limits of x approach infinity? thank you

anonymous · Answer

i believe the answer is "yes"

anonymous · Answer

im guessing 2n is a monomial, im forgetting the terminology right now  but ok haha "thanks" :)

psymon · Answer

For the most part, youre always going to think of constants as minor nuisances as things go to infinity. Sometimes its useful to keep them around though when you started getting into all the other tests for series and such. Its just kind of getting used to what you are and arent allowed to consider when finding if they all converge or diverge.

anonymous · Answer

@Psymon I will deff keep that in mind since for the next sections of sequences and series that i am going to do :)

psymon · Answer

Yep. Sometimes you use the constants for comparison reasons, as a few of the tests involve comparing what you dont know to what you do know. Youll catch on to things :3