Question

Consider the sequence 3/4,4/5,5/6,6/7,... Which statement describes the sequence? The sequence diverges. The sequence converges to 1. The sequence converges to [infinity]. The sequence converges to –[infinity].

Answer 1

The sequence converges to 1.

Explanation:

`(3)/(4), (4)/(5), (5)/(6), (6)/(7)\\\\The \ general \ term = (n -1)/(n)\\\\ \lim_(n \to \infty) ((n -1)/(n)) = \lim_(n \to \infty) (n(1 -(1)/(n)))/(n) = \lim_(n \to \infty) 1 - (1)/(n) = 1 - \lim_(n \to \infty) (1)/(n) = 1`

`[ \lim_(n \to \infty) (1)/(n) = 0]`