12+22+32+...+992=(0+1)1+(1+1)2+....+(98+1)99
=1+1.2+2+...+98.99+99
=(1.2+2.3+...+98.99)+(1+2+3+...+99)
=(1.2+2.3+...+98.99)+4950
đặt A=1.2+2.3+...+98.99
=>3A=1.2.3+2.3.3+...+98.99.3
=1.2.3+2.3(4-1)+...+98.99(100-97)
=1.2.3+2.3.4-1.2.3+...+98.99.100-97.98.99
=98.99.100=970200
=>12+22+32+...+992=970200+4950=975150