Need some help with this Calculus 2 sequence question

Question

Determine whether the sequence converges or diverges. If it converges, find the limit. If it diverges write NONE.

Answer 1

Note that for n large, the expression in square root behaves like n/(25 n), which is 1/25. So you can expect the sequence converges to √(1/25), or 1/5. Indeed, it does, since

lim a_n = lim √((1 + 9/n)/(25 + 9/n)) = √((1 + 0)/(25 + 0)) = √(1/25) = 1/5