In the formula (a + 1) ^ 2 = a ^ 2 + 2A + 1, when a takes 1, 2, 3 respectively N, the following equation can be obtained: (1 + 1) ^ 2 = 1 ^ 2 + 2 * 1 + 1 (2+1)^2=2^2+2*2+1 (3+1)^2=3^2+2*3+1 …… (n+1)^2=n^2+2*n+1 Using the above formulas, conjecture and prove the summation formula, 1 + 2 + 3 + 4 + +n=____ (expressed by the algebraic expression of n)

In the formula (a + 1) ^ 2 = a ^ 2 + 2A + 1, when a takes 1, 2, 3 respectively N, the following equation can be obtained: (1 + 1) ^ 2 = 1 ^ 2 + 2 * 1 + 1 (2+1)^2=2^2+2*2+1 (3+1)^2=3^2+2*3+1 …… (n+1)^2=n^2+2*n+1 Using the above formulas, conjecture and prove the summation formula, 1 + 2 + 3 + 4 + +n=____ (expressed by the algebraic expression of n)

(1+1)^2=1^2+2*1+1 (2+1)^2=2^2+2*2+1 (3+1)^2=3^2+2*3+1 …… (n + 1) ^ 2 = n ^ 2 + 2 * n + 1, that is, 2 ^ 2 = 1 ^ 2 + 2 * 1 + 1 3 ^ 2 = 2 ^ 2 + 2 * 2 + 1 4 ^ 2 = 3 ^ 2 + 2 * 3 + 1 (n + 1) ^ 2 = n ^ 2 + 2 * n + 1 add 2 ^ 2 + 3 ^ 2 + +n^2+(n+1)^2=1^2+2^2+…… +n^2+2*(1+2+… ...