Derivation process of arithmetic sequence summation formula In (a + 1) & sup2; = A & sup2; + 2A + 1, when a goes to 1,2,3 , N, the following n equations can be obtained; （1+1）²=1²——2*1+1 （2+1）²=2²——2*2+1 （3+1）²=3²——2*3+1 …… （n+1）²=n²——2*n+1 When the left and right sides of the n equations are added respectively, the summation formula can be deduced: 1 + 2 + 3 + +N = () is represented by an algebraic expression containing n

Derivation process of arithmetic sequence summation formula In (a + 1) & sup2; = A & sup2; + 2A + 1, when a goes to 1,2,3 , N, the following n equations can be obtained; （1+1）²=1²——2*1+1 （2+1）²=2²——2*2+1 （3+1）²=3²——2*3+1 …… （n+1）²=n²——2*n+1 When the left and right sides of the n equations are added respectively, the summation formula can be deduced: 1 + 2 + 3 + +N = () is represented by an algebraic expression containing n

（1+1）²=2²
（2+1）²=3²
……
After addition and elimination of the repeated terms, (n + 1) & sup2; = 1 & sup2; + 2 * (1 + 2 + 3 +...) +n）+1*n
1+2+3+…… +n=[（n+1）²-n-1]/2=（n²+n）/2=（n+1）n/2