A = 1.2 + 2.3 + 3.4 + + 50.51 = 44 200. Tính S = 1^2 + 2^2

S = 1² + 2² +… + 50²

S = 1.1 + 2.2 + … + 50.50

S = 1.(2 – 1) + 2(3 – 1) + … + 50.(51 – 1)

S = 1.2 – 1 + 2.3 – 2 + 3.4 – 3 + … + 50.51 – 50

S = (1.2 + 2.3 + 3.4 + … + 50.51) – (1 + 2 + 3 + … + 50)

S = 44 200 – \(\frac{{50.\left( {1 + 50} \right)}}{2}\)

S = 44 200 – 1 275

S = 42 925.

Vậy S = 42 925.