The known elements are integer sequence {1}, {2,3}, {4,5,6}, {7,8,9,10} Starting from the second sequence, each number set has one more number than the previous number set, and the minimum number of each number set is 1 larger than the maximum number of the previous number set. Find the sum SN of all numbers in the nth number set

The known elements are integer sequence {1}, {2,3}, {4,5,6}, {7,8,9,10} Starting from the second sequence, each number set has one more number than the previous number set, and the minimum number of each number set is 1 larger than the maximum number of the previous number set. Find the sum SN of all numbers in the nth number set

S1=1
S2+S1=1+2+3
S3+S2+S1=1+2+3+4+5+6
.
Sn-1+Sn-2+...+S1
=1+2+3+...+(n-1)+...+(1+2+3+...+n-1)
=1+2+3+...+(n-1)+...+n*(n-1)/2
= [1+n*(n-1)/2]*[(n-1)/2]/2
=(n^2-n+2)*n*(n-1)/8 (1)
Sn+Sn-1+...+s1=1+2+...+(1+2+...+n)
= (n^2+n+2)*n*(n+1)/8 (2)
(2) - (1) yes
Sn=n*(n^2+1)/2