Clear[a]
a[0]=1.0
a[n_]:=1+1/(1+a[n-1])
Table[{n,(Sqrt[2])-a[n]},{n,1,10,2}]
TableForm[%,TableHeadings->{None,{"n","a_n"}}]

Clear[a]
a[0]=1.0
a[n_]:=1+1/(1+a[n-1])
Table[{n,(Sqrt[2])-a[n]},{n,2,10,2}]
TableForm[%,TableHeadings->{None,{"n","a_n"}}]

Clear[a]
a[0]=1.0
a[n_]:=1+1/(1+a[n-1])
Table[{n,(Sqrt[2])-a[n]},{n,1,10}]
TableForm[%,TableHeadings->{None,{"n","a_n"}}]