Question

[Đinh Đức Hùng]

Tính S = 1² + 2² + 3² + ......... + 100²

Answer 1

[obelish the tormamtor]

5050 nha ban

k minh nha

Answer 2

[Mạnh Lê]

S = 1² + 2² + 3² + ... + 100²

S = 1 .( 2 - 1 ) + 2 .( 3 - 1 ) + 3 .( 4 - 1 ) + ... + 99 .( 100 - 1 ) + 100 .( 101 - 1 ) 

= 1.2 - 1.1 + 2.3 - 1.2 + 3.4 - 1.3 + ... + 99.100 - 1.99 + 100.101 - 1.100

= ( 1.2 + 2.3 + 3.4 + ... + 99.100 + 100.101 ) - ( 1 + 2 + 3 + ... + 99 + 100 ) 

S = [ 1.2.3 + 2.3.(4-1) + 3.4.(5-2) + ... + 100.101.(102-99) ] / 3 + [ ( 100 + 1 ) : 100 / 2 ] 

= [ 1.2.3 + 2.3.4-1 + 2.3+3.4.5-2.3.4 + ... + 100.101.102-99.10.101 ] / 3 + 5050

= 100.101.102/3 + 5050

= 348450