Đáp án`+`Giải thích các bước giải:
` S = 1^2 +2^2 + 3^2 + ... +50^2 `
`= 1.1 + 2.2 + 3.3+ .... + 50.50 `
`= 1.(2-1) + 2(3-1) + 3.(4-1) + ... +50(51-1) `
`= 1.2 -1.1 + 2.3 - 2.1 + 3.4 - 3.1 + .... +50.51 - 50.1 `
`= 1.2 -1 + 2.3 - 2 +3.4 - 3 +...... + 50.51 - 50`
`= (1.2 + 2.3 + 3.4 + ....+50.51) - (1+2+3+....+50) `
Đặt ` (1.2 + 2.3 +.... +50.51)` là ` D`
Ta có `:`
` D = 1.2 + 2.3 + 3.4 + ... +50.51 `
`-> 3D = 1.2.3 + 2.3.3 + 3.4.3 + ....+50.51.3 `
`-> 3D= 1.2.3 + 2.3.(4-1) + 3.4.(5-2) + ..... +50.51.(52-49) `
`-> 3D = 1.2.3 +2.3.4 -1.2.3 +3.4.5 -2.3.4 +....... + 50.51.52 -49.50.51 `
`-> 3D = 50.51.52 `
`-> 3D = 132600`
`-> D = 44200 `
Đặt ` (1+2+3+...+50) ` là `C`
Ta có:
` C = 1+2+3+...+50 `
`= (50+1) .50 : 2`
`= 1275`
Ta có :
` S = (1.2 + 2.3 + 3.4 + ....+50.51) - (1+2+3+....+50) `
`-> S = C - D `
`= 44200 - 1275 `
`= 42952 `
Vậy `S = 42952 `
