14. In the formula (a + 1) 2 = A2 + 2A + 1, when a takes 1,2,3 , N, we can get the following n equations (1 + 1) 2 = 12 + 2 × 1 + 1 （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 By adding the left and right sides of these n equations, the summation formula can be derived 1+2+3…… +N = (expressed in an algebraic expression containing n)

14. In the formula (a + 1) 2 = A2 + 2A + 1, when a takes 1,2,3 , N, we can get the following n equations (1 + 1) 2 = 12 + 2 × 1 + 1 （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 By adding the left and right sides of these n equations, the summation formula can be derived 1+2+3…… +N = (expressed in an algebraic expression containing n)

（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
Add the left and right sides of these n equations,
Some of the items offset
（n+1）^2=2【1+2+3…… +n】+n +1
【1+2+3…… +n】＝[（n+1)n]/2