Question

Tính: 1*2 + 2*3 + 3*4 + ........ + 50*51

  1² + 2² + 3² + ....... + 50²

Answer 1

1/ S=1.2+2.3+3.4+...+50.51

=> 3S=1.2.3+2.3.3+3.4.3+...+50.51.3

=> 3S=1.2.3+2.3.(4-1)+3.4.(5-2)+...+50.51(52-49)

=> 3S=(1.2.3+2.3.4+3.4.5+...+50.51.52)-(1.2.3+2.3.4+...+49.50.51)

=> 3S=50.51.52 => S=50.51.52:3=44200

Đáp số: 44200

2/ A=1²+2²+3²+4²+...+50² = 1(2-1)+2(3-1)+3(4-1)+...+50(51-1)

=> A=(1.2+2.3+3.4+...+50.51)-(1+2+3+...+50)

=> A=S-\(\frac{50\left(50+1\right)}{2}\)=44200-1275

A=42925

Đáp số: 42925