A=1+4+9+......+2401+2500
A=12+22+32+...........+492+502
A=1.(2-1)+2.(3-1)+3.(4-1)+.............+49.(50-1)+50.(51-1)
A=1.2-1+2.3-2+3.4-3+.............+49.50-49+50.51-50
A=(1.2+2.3+3.4+............+49.50+50.51)-(1+2+3+.........+49+50)
A=\(\frac{50.51.52}{3}-\frac{50.\left(50+1\right)}{2}\)
A=44200-1275
A=42925