and you know that 1/n converges...so by comparison, tan(1/n)/(1+n) must also converge
The SEQUENCE with general term 1/n converges, does the series?
Well.. sin(1/n) is approximately 1/n for large n. I would do some sort of error estimate for tan(1/n) = 1/n + error to see if the the series CONVERGES absolutely. (Error estimates for sin(1/n) may suffice.)
Watch out for comparing to the famously DIVERGING harmonic series.
d_leet, ok tan(x) does approach infinity when cos(x) approaches 0
"The harmonic series diverges, albeit slowly, to infinity"