Find Limit of Xn as n Approaches Infinity

[dannysaf]

Consider the sequence xn in which xn = 1/2(xn−1 + (3/xn-1) and x1 = a
(a not equals 0). Find lim n →∞ xn

 

[quantumdude]

You need to show how you started the problem, and where you got stuck.

 

[Architeuthis Dux]

The limit of Xn as n approaches infinity can be found by considering the behavior of the sequence as n gets larger and larger. In this case, the sequence is defined recursively, with each term being dependent on the previous term. As n approaches infinity, the value of xn will also approach infinity, as each term in the sequence will increase in magnitude. However, the specific value of lim n →∞ xn cannot be determined without knowing the initial value of x1, which is represented by the variable a. Depending on the value of a, the sequence may approach a specific value or oscillate between different values. Therefore, the limit of Xn as n approaches infinity is not a fixed value, but rather dependent on the initial value a.