- #1

kwal0203

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## Homework Statement

Use a comparison test to determine whether this series converges:

[tex] \sum_{x=1}^{\infty }\sin ^2(\frac{1}{x}) [/tex]

## Homework Equations

## The Attempt at a Solution

At small values of x:

[tex] \sin x\approx x [/tex]

[tex] a_{x}=\sin \frac{1}{x} [/tex]

[tex] b_{x}=\frac{1}{x} [/tex]

[tex] \lim \frac{a_{x}}{b_{x}}=\frac{\sin \frac{1}{x}}{\frac{1}{x}}=1 [/tex]

Since 1/x diverges so does sin(1/x).

Can I use this same method to solve the question above? ( i.e. sin^2(1/x) )