Does e^n·sin(n) converge and does e^(2n)/4^n converge?

[hytuoc]

Would someone please help me w/ the problems below? Thanks so much
Determine whether the sequence converges or diverges, n, if it converges, find lim as n approaches infinity of "an" (subscript "n")
1) an= e^(n) sin(n)
2) an = e^(2n)/ [4^n]

 

[Gokul43201]

What determines whether a series converges, or not ?

(what tests are there to check for convergence ?)

 

[hytuoc]

more like finding a derivative of those

 

[phoenixthoth]

Would someone please help me w/ the problems below? Thanks so much
Determine whether the sequence converges or diverges, n, if it converges, find lim as n approaches infinity of "an" (subscript "n")
1) an= e^(n) sin(n)
2) an = e^(2n)/ [4^n]

I'm not sure if you titled this thread right; this is a sequence question but that's ok.

One way to get a handle on convergence is to plug in a few values for n and see if there is a pattern in the higher n (as n approaches infinity). Try this for 1) and see what happens. I think it diverges.

For 2) you can do the same thing and/or rewrite it first into
E=e^2
an=(E/4)^n
then you should have a theorem which states that since E/4>1, the sequence diverges.