sum_(n=0)^oo (n+10)/(10n+1) Determine the convergence or divergence of the series.

sum_(n=0)^oo(n+10)/(10n+1)
For the series a_n=(n+10)/(10n+1)
a_n=(1+10/n)/(10+1/n)
lim_(n->oo)a_n=lim_(n->oo)(1+10/n)/(10+1/n)
=1/10!=0
As per the n'th term test for divergence,
If lim_(n->oo)a_n!=0 , then sum_(n=1)^ooa_n diverges
So, the series diverges.