Calculate 1 + (1 + 2) + (1 + 2 + 3) + +(1+2+3+… +n).

Calculate 1 + (1 + 2) + (1 + 2 + 3) + +(1+2+3+… +n).


∵1+2+3+… +n=n(n+1)2=n2+n2,∴1+(1+2)+(1+2+3)+… +(1+2+3+… +n)=12(1+12+2+22+3+32+… +n+n2)=12[(1+2+3+… +n)+(12+22+32+… +n2)]=12•[n(n+1)2+n(n+1)(2n+1)6]=n(n+1)4+n(n+1)(2n+1)12.



1 square + 2 square + 3 square +. + (n-1) square + n square =?


1 square + 2 square + 3 square +. + (n-1) square + n square
=n(n+1)(2n+1)/6



① Square of M (a-b) * (C-A) + n (A-C) * (B-A)
② If 2A + B = 0.2, ab = 8, then the three sides of 2a, the square of B + the three sides of a, the three sides of B=


The original formula = m (a-b) &# 178; (C-A) - n (C-A) (a-b) &# 178;
=(a-b)²(c-a)(m-n)
The original formula = A & # 178; B & # 178; (2a + b)
=(ab)²(2a+b)
=8²×0.2
=12.8