Toán Tính A = 1.2 + 2.3 + 3.4 + … + n.(n + 1) Ooooooooooooooo 17/09/2021 By Eliza Tính A = 1.2 + 2.3 + 3.4 + … + n.(n + 1) Ooooooooooooooo
Đáp án: $\rm A=\dfrac{n.(n+1).(n+2)}{3}$ Giải thích các bước giải: $\rm A=1.2+2.3+3.4+…+n.(n+1)$ $\rm 3A=1.2.3+2.3.3+3.4.3+…+n.(n+1).3$ $\rm 3A=1.2.3+2.3.(4-1)+3.4.(5-2)+…+n.(n+1).(n+2-n+1)$ $\rm 3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+…+n.(n+1).(n+2)-n.(n+1).(n-1)$ $\rm 3A=n.(n+1).(n+2)$ $\rm A=\dfrac{n.(n+1).(n+2)}{3}$ Trả lời
$\text{Đáp án + Giải thích các bước giải:}$ `A=1.2+2.3+3.4+….+n.(n+1)` `=>3A=1.2.3+2.3.3+3.4.3+….+n.(n+1).3` `=>3A=1.2.3+2.3.(4-1)+3.4.(5-2)+….+n.(n+1).(n+2-n+1)` `=>3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+…+n.(n+1).(n+2)-n.(n+1).(n-1)` `=>3A=n.(n+1).(n+2)` `=>A=(n(n+1)(n+2))/(3)` Trả lời
Đáp án:
$\rm A=\dfrac{n.(n+1).(n+2)}{3}$
Giải thích các bước giải:
$\rm A=1.2+2.3+3.4+…+n.(n+1)$
$\rm 3A=1.2.3+2.3.3+3.4.3+…+n.(n+1).3$
$\rm 3A=1.2.3+2.3.(4-1)+3.4.(5-2)+…+n.(n+1).(n+2-n+1)$
$\rm 3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+…+n.(n+1).(n+2)-n.(n+1).(n-1)$
$\rm 3A=n.(n+1).(n+2)$
$\rm A=\dfrac{n.(n+1).(n+2)}{3}$
$\text{Đáp án + Giải thích các bước giải:}$
`A=1.2+2.3+3.4+….+n.(n+1)`
`=>3A=1.2.3+2.3.3+3.4.3+….+n.(n+1).3`
`=>3A=1.2.3+2.3.(4-1)+3.4.(5-2)+….+n.(n+1).(n+2-n+1)`
`=>3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+…+n.(n+1).(n+2)-n.(n+1).(n-1)`
`=>3A=n.(n+1).(n+2)`
`=>A=(n(n+1)(n+2))/(3)`