問有關特種級數之數學問題???

1x99 + 2x98 + 3x97 + ... + 49x51 + 50x50 + 51x49 + ... + 99x1= 2(1x99 + 2x98 + 3x97 + ... + 49x51) + 50x50= 2[1(100-1) + 2(100-2) + 3(100-3) + ... + 49(100-49)] + 50x50= 2[(100 - 1²) + (200 - 2²) + (300 - 3²) + ... + (4900 - 49²)] + 2500= 2[(100 + 200 + 300 + ... + 4900) - (1² + 2² + 3² + ... + 49²)] + 2500= 2[(100+4900)49/2 - 49(49+1)(2*49+1)/6] + 2500= 2[122500 - 40425] + 2500= 166650