Answer
Diverges
Work Step by Step
$\lim _{n\rightarrow \infty }\dfrac {n+10}{10n+1}=\dfrac {1+\dfrac {10}{n}}{10+\dfrac {1}{n}}=\dfrac {1+0}{10+0}=\dfrac {1}{10}\neq 0$
$\Rightarrow \sum ^{\infty }_{n=0}\dfrac {n+10}{10n+1}$ diverges
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