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.
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https://math.stackexchange.com/questions/947268/runge-kutta-methods-and-butcher-tableau – Ryan Howe Dec 09 '20 at 00:56
