sequence convergence of sqrt(2)

I am having some difficulties converging this sequence to sqrt(2).

the values are not computing properly and I am not sure why.

N=randi(100);

X1=1;

for k=[2:1:N]

Xk= 0.5.*(k-1)+(2/k-1);

end

terms=linspace(2,Xk,N)

Answer 1

[Alan Stevens]

I think you probably want

X(k) = 0.5*X(k-1) + 1/(2*X(k-1));

with

X(1) = 1;