What is a convergent sequence and a divergent sequence?

Theorem stated the following: "If we apply a continuous function to the terms of a convergent sequence, the...?

• "If we apply a continuous function to the terms of a convergent sequence, the result is also convergent." -If lim (as n approaches infinity) of a "sub" n = L and ...show more

• Answer:

  Your examples are a bit different. For e^x, you don't have a convergent sequence to begin with if you try to go off to infinity. For ln(x) you have a similar problem if you go that way, but you might try to converge to zero, which seems like a contradiction. But actually, the theorem only goes through if the function is continuous at L, and ln(x) is not continuous at zero.