Determine whether the following series converge or diverge
SUM (1+sin(n))/(3^n) from n=1 to inf

Question

Determine whether the following series converge or diverge
SUM (1+sin(n))/(3^n) from n=1 to inf

anonymous · Answer

I think I'm having a hard time figuring out what test to use on problems like these. I took the limit and I got 0, but thats not helping me

zarkon · Answer

use a comparison test

anonymous · Answer

For the comparison test, I usually only use that when I think i can compare to a p series, ex 1/n^p but i have #/3^n so I don't see how that would work. ..... Of course thats the only way I know how to use it anyway.

zarkon · Answer

if you had something like this

$$\sum_{n=1}^{\infty}\frac{a}{3^n}$$

it would converge (geometric sum)

anonymous · Answer

so i'm comparing it to a geometric sum...is there another way. I'm not quite getting that idea.

zarkon · Answer

you could try a ratio or root test...but comparison is the best way

anonymous · Answer

tried ratio got stuck at lim 1+sin(1)cos(n)+cos(1)/9

anonymous · Answer

but then again I can think about it and I know that, that is less than 1 (since i know the numerator will not be greater than 9.

anonymous · Answer

am I correct if I do it that way?

anonymous · Answer

your numerator will not be greater than two

anonymous · Answer

so make it two for a comparison as zarkon suggested