Question

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
an = ln(n + 4) -ln n

Answer 1

HI!!

Answer 2

write it as
\[\ln(\frac{n+4}{n})\] then you see it converges to \(\ln(1)=0\)

Answer 3

Thanks so much!

Answer 4

For a more rigorous approach, you might want to establish that the sequence is bounded and monotonic. Any bounded/monotonic sequence must converge (see here: ` http://en.wikipedia.org/wiki/Monotone_convergence_theorem `).