Question

If a sequence has limit k, then the sequence has limit _________. Use this fact together with l'Hopital's rule to compute the limit of the sequence given by___________.

Answer 1

If a sequence has limit k, then the sequence has limit k as well. To use l'Hopital's rule to compute the limit of a sequence, express the sequence as a fraction, take the derivatives of the numerator and denominator, and compute their limits separately.

Step-by-step explanation:

If a sequence has limit k, then the sequence has limit k as well. This is because the limit of a sequence represents the value that the terms of the sequence approach as the index of the terms approaches infinity. Since the limit of the sequence is k, it means that the terms of the sequence get closer and closer to k as the index increases.

To use l'Hopital's rule to compute the limit of a sequence, you first need to express the sequence as a fraction with a numerator and a denominator. Then, take the derivative of both the numerator and denominator and compute their limits separately. Finally, take the limit of the original fraction.