Question #e7ab8

2 Answers
Sep 25, 2015

It is divergent

Explanation:

All the terms of this sequence are greater than one. Hence as n-> oo, a_n !=0. Sequence does not therefore converge. It diverges.

Sep 25, 2015

The sequence converges to 2.

Explanation:

The sequence is increasing and bounded (by 2) so it must converge.

Let b_n = a_(n+1), i.e. b_n=sqrt(2+a_n)

b_n must converge to the same limit as a_n, so, calling the limit L, we have L = sqrt(2+L).

Solving the equation gets us L=2.