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Find the following rates of convergence.

[tex]

\lim_{n\rightarrow infinity} sin(1/n) = 0

[/tex]

My thought would be to do the following

[tex]

|sin(1/n) - 0| <= 1

[/tex]

But the book says to get a rate in the form [tex]1/n^p[/tex]

The following also gives me trouble.

[tex]

\lim_{n\rightarrow infinity} sin(1/n^2) = 0

[/tex]

which seems like it should converge faster than the the first one.