And then a? (n)=k+√...=k+a(n- 1), which is a general formula.

There is a sentence in the title "As n becomes great", that is, when n is great (tends to infinity),

The expressions of a(n) and a(n- 1) are actually the same.

Answer? (n)=k+a(n), the solution is

a(n)=[ 1 √( 1+4k)]/2

A(n)>0, the minus sign is discarded.

a(n)=[ 1+√( 1+4k)]/2

If the last expression of k is given in this question, it is necessary to prove the convergence of the sequence {a(n)} before using the above method, but this question gives the case of k= 1 and k=2, which is similar to mathematical induction, so it is not necessary to prove the convergence of the sequence.