Find limit of sequence xₙ = ½(xₙ₋₁ + 3/xₙ₋₁) with x₁ = a

[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

 

[VeeEight]

If you do not need to show that the limit actually exists, then you can go straight to finding it algebraically. Notice that the lim x_n is the same as lim x_(n-1) (as n tends to infinite). You can use this to find your limit.