2 câu trả lời
Đáp án+Giải thích các bước giải:)
@danggiabao0
Đặt `A`=`1^2`+...+`100^2`
`A`=`1`.`1`+...+`100`.`100`
`A`=`1`.`(2-1)`+....+`100`.`(101-1)`
`A`=`1`.`2`-`1`+...+`100`.`101`-`100`
`A`=`(1.2+...+100.101)`-`(1+...+100)`
Đặt `B`=`(1.2+...+100.101)`
`3``B`=`1`.`2`.`3`+...+`100`.`101`.`3`
`3``B`=`1`.`2`.`(3-0)`+...+`100`.`101`.`(102-99)`
`3``B`=`1`.`2`.`3`+...+`100`.`101`.`102`-`99`.`100`.`101`
`3``B`=`100`.`101`.`102`
`B`=`{100.101.102}/3`
Đặt `C`=`(1+...+100)`
`C`=`(100+1)`.`{100}/2`=`5050`
`A`=`B`-`C`=`338350`
` Huy `
` 1^2+2^2+...+n^2 `
` = 1+ 2.(1+1) + 3.(2+1) +...+ n(n-1 +1) `
` =1 + 1.2 +2 + 2.3 + 3 +...+ (n-1).n + n `
` = (1 + 2 +3 +....+n) + [1.2 + 2.3 + 3.4 + ......+ (n-1)n] `
` = \frac{n.(n+1)}{2} + \frac{(n-1).n.(n+1)}{3} `
` => 1^2 +2^2 + ... + 100^2 `
` = \frac{100.(100+1)}{2} + \frac{(100-1).100.(100+1)}{3} `
` = \frac{100.101}{2} + \frac{99.100.101}{3} `
` = 5050+333300=338350 `
