The n power of binomial theorem (a+b) = cn0anb0+cn1a (n-1) b1+...+cnnabn (if you can't type it out, you have to paste it, understand). The expansion coefficient method is positive. Mathematical induction is actually to find out whether it is true or not. The proof of mathematical induction must meet two conditions: 1, and the existence of R belongs to n, so that AR = (a+b) R, AR+1= (a+b) R+1; 2.A 1 = (a+b) 1 holds. Then the assumed power of (a+b) = cn0anb0+cn1a (n-1). The formula b1+...+cnnabn can be established. The concrete proof is as follows: let (a+b) r = cr0arb0+Cr1a (r-1) b1+... expand it into (a+b) rxa+(a+b) rxb, and then deduce c (r+). B 2+...+C (r+1) (r+1) A 0br+1,and only C (r+1) A 0br+1B0 and. It is consistent with the assumption that (r+ 1) brings R, so the first condition is proved. The second condition (A+B) 1 = A+B is easy to prove, so the original assumption is a+b) r = cr0arb0+Cr1a.