The coefficient of Adam Bashforth method

Question

When using Adams-Bashforth method, after integrating the polynomial of k-th order, we obtain a linear combination of $f(t_n,y_n),f(t_{n+1},y_{n+1}),…,f(t_{n+k},y_{n+k})$.
However, I am curious about why the sum of all the coefficients is always 1.
Below is the formulae for k<4 from wikipedia. So please tell me why we always get 1 after summing up the coefficients.

Answer 1

Think about what the method should look like for a constant f, e. g. f(t,y)=1 :)