Show convergence using comparison test on sin(1/n)

[ciarax]

Homework Statement

a) Test the following series for convergence using the comparison test
:
sin(1/n)

Explain your conclusion.

Homework Equations

The Attempt at a Solution

i must show f(x)<g(x) in order for it to converge other wise divergence.

g(x) = 1/n

sin(1/n) > 1/n always therefore the series is divergent.
is this correct?

 

[micromass]

sin(1/n) > 1/n

How did you obtain this inequality?? It isn't correct.

 

[ciarax]

it was an attempt. i was looking back on my notes and thought that might be right :/ do you have any idea how to complete this?

 

[micromass]

The inequality sin(1/n) > 1/n might not hold, but it can be modified in something that does hold.

 

[ciarax]

does this prove that it is divergent? or how do i go about proving if its convergent/divergent using the comparison test?

 

[Joffan]

For large n, sin(1/n) ≈ 1/n. So use that to find your inequality.

 

[ciarax]

does that give sin(1/n) > 1/2n?

 

[Joffan]

It does for me.

 

[ciarax]

so using that its divergent? thanks :)