Question

tinh 1^2+2^2+3^2+4^2+...+100^2

cach giai

 

Answer 1

S = 1² + 2² + 3² + ..... + 100²

= 1.(2-1) + 2.(3-1) + .... + 100.(101-1)

= 1.2 + 2.3 + ....... + 100.101 - (1+2+3+...+100)

Đặt A = 1.2 + 2.3 + ... + 100.101

3A = 1.2.(3-0) + 2.3.(4-1) + .... + 100.101.(102-99)

3A = 1.2.3  + 2.3.4-1.2.3 + ... +100.101.102-99.100.101

3A = 100.101.102

A = 100.101.102 : 3 = 33367034

S = 33367034 - 5050

S = 33361984

 

Answer 2

S = 1² + 2² + 3² + ..... + 100²

= 1.(2-1) + 2.(3-1) + .... + 100.(101-1)

= 1.2 + 2.3 + ....... + 100.101 - (1+2+3+...+100)

Đặt A = 1.2 + 2.3 + ... + 100.101

3A = 1.2.(3-0) + 2.3.(4-1) + .... + 100.101.(102-99)

3A = 1.2.3  + 2.3.4-1.2.3 + ... +100.101.102-99.100.101

3A = 100.101.102

A = 100.101.102 : 3 = 33367034

S = 33367034 - 5050

S = 33361984

 

Answer 3

S = 1² + 2² + 3² + ..... + 100²

= 1.(2-1) + 2.(3-1) + .... + 100.(101-1)

= 1.2 + 2.3 + ....... + 100.101 - (1+2+3+...+100)

Đặt A = 1.2 + 2.3 + ... + 100.101

3A = 1.2.(3-0) + 2.3.(4-1) + .... + 100.101.(102-99)

3A = 1.2.3  + 2.3.4-1.2.3 + ... +100.101.102-99.100.101

3A = 100.101.102

A = 100.101.102 : 3 = 33367034

S = 33367034 - 5050

S = 33361984