kwal0203
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Homework Statement
Use a comparison test to determine whether this series converges:
\sum_{x=1}^{\infty }\sin ^2(\frac{1}{x})
Homework Equations
The Attempt at a Solution
At small values of x:
\sin x\approx x
a_{x}=\sin \frac{1}{x}
b_{x}=\frac{1}{x}
\lim \frac{a_{x}}{b_{x}}=\frac{\sin \frac{1}{x}}{\frac{1}{x}}=1
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) )