求下列数字方阵中所有数的和1,2,3,4,···,18,19,202,3,4,5,···,19,20,213,4,5,6,···,20,21,224,5,6,7,···,21,22,23···········20,21,22,23,···,37,38,39
问题描述：
求下列数字方阵中所有数的和
1,2,3,4,···,18,19,20
2,3,4,5,···,19,20,21
3,4,5,6,···,20,21,22
4,5,6,7,···,21,22,23
···········
20,21,22,23,···,37,38,39
答
第一行之和S1=210=210+20*0第二行之和S2=210+21-1=210+20*1第三行之和S3=210+22+21-2-1=210+20*2.由此可推,第n行之和Sn=210+20*(n-1)所有n行的总和S总=210*n+20*[1+2+3+.+(n-1)]=210*n+20*(n-1)n/2=210n+10n(n-1)=10...