Does the limit from 0 to infinity of (1+sin n)/10^n converge or diverge?

i thought An= (1+sin n)/10^n) and Bn= 1/10^n but (1/10)^n converges while An>Bn so the comparison test does not work. so then i tried the limit comparison test and got limit n-> infinity of 1+sin n...... idk where i went wrong ):