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lax1113
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Infinite series sin(1/n)/n ?
does the series (sin (1/n)) / sqrt ( n ) converge or diverge? (series from n = 1 to infinity...)
I thought that for this we could do a comparison of sin (1/n) to a finite number. Let's say we use the number -2. -2 is less than sin(1/n) for all n. With that being said, -2/ sqrt( n ) diverges, as it is a p series with p less than 1.
But, this series actually converges... what did I do wrong?
Homework Statement
does the series (sin (1/n)) / sqrt ( n ) converge or diverge? (series from n = 1 to infinity...)
Homework Equations
The Attempt at a Solution
I thought that for this we could do a comparison of sin (1/n) to a finite number. Let's say we use the number -2. -2 is less than sin(1/n) for all n. With that being said, -2/ sqrt( n ) diverges, as it is a p series with p less than 1.
But, this series actually converges... what did I do wrong?