First, you ask me for help. Thank you for your trust in me. In fact, I haven't answered questions about knowledge for a long time. I went into Baidu today and found someone asking for help, so I took a look. Because I haven't done math problems for a long time, my hands are born. So the following process is given for your reference.

Solution: We can use a property of the sum of the first n terms of arithmetic progression: it must be quadratic, and the constant coefficient term is 0, that is,

The sum of the first n terms is sn = an 2+bn, where a and b are constants, and then it is relatively simple. The process is as follows:

sm+n=a(m+n)^2+b(m+n)…………( 1)

Sm=Am^2+Bm=n………………(2)

Sn=An^2+Bn=m………………(3)

(2)-(3)

A(m+n)(m-n)+B(m-n)=n-m

that is

[A(m+n)+B+ 1](m-n)=0, that is, [A(m+n)+B](m-n)=-(m+n).

sm+n=a(m+n)^2+b(m+n)=[a(m+n)+b](m-n)=-(m+n)