Question

determine whether the series is absolutely convergent, conditionally convergent, or divergent sin(n)/3^n convergent

Answer 1

absolutely convergent

Explanation:

given data

sin(n)/3^n

solution

we have given term
`(sin(n))/(3^n)`

when n = 1

and we know that

value of sin(n) ≤ 1

so that we can say that

`(sin(n))/(3^n)` ≤
`(1)/(3^n)` or
`((1)/(3))^n`

here
`(1)/(3^n)` is converges this is because common ratio in geometric series

here r is
`(1)/(3)` and here it satisfy that -1 < r < 1

so it is converges

and

`(sin(n))/(3^n)` is also similar

so it is converges

and here no
`(-1)^n` term is

so we can say series is absolutely convergent