tinh : F=100.1+99.2+98.3+…+2.99+1.100 giup minh voi

`F = 1*100 + 2*99 + 3*98 + 4*97 + … + 97*4 + 98*3 + 99*2 + 100 *1`

 

`F = 1*100 + 2*(100 – 1) + 3*(100 – 2) + 4*(100 – 3) + … + 97*(100 – 96) + 98*(100 – 97) + 99*(100 – 98) + 100 *(100 – 99)`

 

`F = 1*100 + (2*100 – 1*2) + (3*100 – 2*3) + (4*100 – 3*4) + … + (97*100 – 96*97) + (98*100 – 97*98) + (99*100 – 98*99) + (100*100 – 99*100)`

 

`F = (1*100 + 2*100 + 3*100 + 4*100 + … + 97*100 + 98*100 + 99*100 + 100*100) – (1*2 + 2*3 + 3*4 + … + 96*97 + 97*98 + 98*99 + 99*100)`

 

`F = 100*(1 + 2 + 3 + 4 + … + 97 + 98 + 99 + 100) – (1*2 + 2*3 + 3*4 + … + 96*97 + 97*98 + 98*99 + 99*100)`

 

– Đặt `B = 1 + 2 + 3 + 4 + … + 97 + 98 + 99 + 100`

`C = 1*2 + 2*3 + 3*4 + … + 97*98 + 98*99 + 99*100`

 

– Tổng `B` có số số hạng là :

          `(100 – 1) : 1 + 1 = 100` (số)

– Tổng `B` có giá trị là :

        `(1 + 100) * 100 : 2 = 5050`

 

– Ta có :

`C = 1*2 + 2*3 + 3*4 + … + 97*98 + 98*99 + 99*100`

 

`3C = 1*2*3 + 2*3*3 + 3*4*3 + … + 97*98*3 + 98*99*3 + 99*100*3`

 

`3C = 1*2*3 + 2*3*(4 – 1) + 3*4*(5 – 2) + … + 97*98*(99 – 96) + 98*99*(100 – 97) + 99*100*(101 – 98)`

 

`3C = 1*2*3 + (2*3*4-2*3*1) + (3*4*5 – 3*4*2) + … + (97*98*99 – 97*98*96) + (98*99*100- 98*99*97) + (99 *100*101- 99*100*98)`

 

`3C = (1*2*3 – 2*3*1) + (2*3*4 – 3*4*2) + … + (97*98*99 – 98*99*97) + (98*99*100 – 99*100*98) + 99*100*101`

 

`3C = 0 + 0 + … + 0 + 0 + 99*100*101`

 

`3C = 99*100*101`

 

`=> C = (99*100*101)/3 = 333300` 

 

– Ta lại có :

`F= 100B – C`

 

`F = 100*5050 – 333300`

 

`F = 505000 – 333300`

 

`F = 171700`

Trả lời