What is the limit of as tends to infinity? To my mind, it's either or . And I'm leaning towards , but I'm not sure.
Thank you very much.
I assume you are using base 10 in your logarithms. The limit is zero.
This simplifies to:
If you are using base e. A similar simplification will come out of base 10. So the limit is a little more obvious.
If you apply the condensation test with e in place of 2, it tells you that the convergence of is equivalent to that of , which converges by comparison with .
Of course, if the logs are to base 10 then the same argument will work. You just replace 2 by 10 instead of e.