$\dfrac{1}{1.2.3}$ + $\dfrac{1}{2.3.4}$ + $\dfrac{1}{3.4.5}$ +…+ $\dfrac{1}{100.101.102}$ 20/08/2021 Bởi Brielle $\dfrac{1}{1.2.3}$ + $\dfrac{1}{2.3.4}$ + $\dfrac{1}{3.4.5}$ +…+ $\dfrac{1}{100.101.102}$
Đáp án+Giải thích các bước giải: $Đặt A=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+…+\dfrac{1}{100.101.102}\\=>2A=\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+\dfrac{2}{3.4.5}+…+\dfrac{2}{100.101.102}\\=\dfrac1{1.2}-\dfrac1{2.3}+\dfrac1{2.3}-…+\dfrac1{100.101}-\dfrac1{101.102}\\=\dfrac1{2}-\dfrac1{101.102}\\=\dfrac{2575}{5151}\\=>A=\dfrac{\dfrac{2575}{5151}}{2}=\dfrac{2575}{10302}$ Bình luận
Đáp án: ` 1/(1.2.3)+1/(2.3.4)+1/(3.4.5)+…+1/(100.101.102)` `= 1/2(2/(1.2.3)+2/(2.3.4)+2/(3.4.5)+…+2/(100.101.102))` `= 1/2((3-1)/(1.2.3)+(4-2)/(2.3.4)+(5-3)/(3.4.5)+…+(102-100)/(100.101.102)` `=1/2(1/(1.2)-1/(2.3)+1/(2.3)-1/(3.4)+1/(3.4)-1/(4.5)+…+1/(100.101)-1/(101.102))` `=1/2(1/2-1/10302)` `=1/2 . 2575/5151` `=2575/10302` Bình luận
Đáp án+Giải thích các bước giải:
$Đặt A=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+…+\dfrac{1}{100.101.102}\\=>2A=\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+\dfrac{2}{3.4.5}+…+\dfrac{2}{100.101.102}\\=\dfrac1{1.2}-\dfrac1{2.3}+\dfrac1{2.3}-…+\dfrac1{100.101}-\dfrac1{101.102}\\=\dfrac1{2}-\dfrac1{101.102}\\=\dfrac{2575}{5151}\\=>A=\dfrac{\dfrac{2575}{5151}}{2}=\dfrac{2575}{10302}$
Đáp án:
` 1/(1.2.3)+1/(2.3.4)+1/(3.4.5)+…+1/(100.101.102)`
`= 1/2(2/(1.2.3)+2/(2.3.4)+2/(3.4.5)+…+2/(100.101.102))`
`= 1/2((3-1)/(1.2.3)+(4-2)/(2.3.4)+(5-3)/(3.4.5)+…+(102-100)/(100.101.102)`
`=1/2(1/(1.2)-1/(2.3)+1/(2.3)-1/(3.4)+1/(3.4)-1/(4.5)+…+1/(100.101)-1/(101.102))`
`=1/2(1/2-1/10302)`
`=1/2 . 2575/5151`
`=2575/10302`