Question

10+20+30+.....+1230=...........
7+14+21+.....+315=.............

Answer 1

10+20+30+...1230=10(1+2+3+....123)=10*123*(123+1)/2=1230*62=76260
7+14+21+....315=7(1+2+3+....+45)=7*45*(45+1)/2=315*23=7245

Answer 2

 [tex]dam\, factor\,comun\,pe\,10...\\10\cdot(\underbrace{1+2+3+...+123}_{suma \,Gauss})=10\cdot\frac{123\cdot124}{2}=\\=5*123*124=76260\surd\surd\\ dam\,factor\,comun\,pe\,7...\\7\cdot(1+2+3+...45)=7\cdot\frac{45\cdot46}{2}=\\ =7*45*23=7245\surd\surd [/tex]