Thread: Sequence Limits

This is the same as finding regular limits, but only using integers, right?

The problem is: a_n=[ln(2+e^n)]/3n

How do I solve it?

Originally Posted by schnek

This is the same as finding regular limits, but only using integers, right?

The problem is: a_n=[ln(2+e^n)]/3n

How do I solve it?

You could use L'Hopital's Rule here. Observe that both numerator and denominator go to infinity as n goes to infinity.

Then the ratio will approach the ratio of the derivatives:

Originally Posted by schnek

This is the same as finding regular limits, but only using integers, right?

The problem is: a_n=[ln(2+e^n)]/3n

How do I solve it?

Or merely note that . The second term in a senes "doubly" tends to zero. The numerator tends towards and the denominator is getting unboundedly large.