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## Homework Statement

Ʃ[itex]^{∞}_{n=1}[/itex] [itex]\frac{sin(1/n}{\sqrt{n}}[/itex]

## Homework Equations

## The Attempt at a Solution

lim[itex]_{n→∞}[/itex] [itex]\frac{sin(1/n}{\sqrt{n}}[/itex]= lim[itex]_{n→∞}[/itex] [itex]\frac{-2cos(1/n)}{n^{3/2}}[/itex] with l'hospital rule = 0

since lim[itex]_{n→∞}[/itex]=0 therefore the series is convergent

Do you think I did this right?