12.5.10 Olympic Algebra

Condition: let for the sequence \ (\ left \ {c_ {n} \ right \} \) there is a ratio: \ [c_ {n+1} = \ sqrt {c_}+\ sqrt {n-1}, n \ geq 1, c_ {0}> 0, 0, 0, 0, 0, 0, 0 c_ {1}> 0 \] prove that \ (c_ {n} \) converges and find its limit.