1/1x2x3 + 1/2x3x4 + 1/3x4x5 + … + 1/2018x2019x2020 30/09/2021 Bởi Reagan 1/1x2x3 + 1/2x3x4 + 1/3x4x5 + … + 1/2018x2019x2020
$\dfrac{1}{1.2.3} + \dfrac{1}{2.3.4} + \dfrac{1}{3.4.5} + …. + \dfrac{1}{2018.2019.2020}$ $= \dfrac{1}{1.2} – \dfrac{1}{2.3} + \dfrac{1}{2.3} – \dfrac{1}{3.4} + \dfrac{1}{3.4} – \dfrac{1}{4.5} + …. + \dfrac{1}{2018.2019} – \dfrac{1}{2019.2020}$ $= \dfrac{1}{2} – \dfrac{1}{4078380}$ $= \dfrac{2039189}{4078380}$ Bình luận
Đặt A=1/1x2x3 + 1/2x3x4 + 1/3x4x5 + … + 1/2018x2019x2020 ⇒ 2A = 2/1x2x3 + 2/2x3x4 + 2/3x4x5 + … + 2/2018x2019x2020 ⇒ 2A= -1/1×2 + 1/2×3 – 1/2×3 +1/3×4 – 1/3×4 + 1/4×5 + … -1/2018×2019 + 1/2019×2020 ⇒ 2A = -1/1×2 + 1/2019×2020 A = 2039189/4078380 Bình luận
$\dfrac{1}{1.2.3} + \dfrac{1}{2.3.4} + \dfrac{1}{3.4.5} + …. + \dfrac{1}{2018.2019.2020}$
$= \dfrac{1}{1.2} – \dfrac{1}{2.3} + \dfrac{1}{2.3} – \dfrac{1}{3.4} + \dfrac{1}{3.4} – \dfrac{1}{4.5} + …. + \dfrac{1}{2018.2019} – \dfrac{1}{2019.2020}$
$= \dfrac{1}{2} – \dfrac{1}{4078380}$
$= \dfrac{2039189}{4078380}$
Đặt A=1/1x2x3 + 1/2x3x4 + 1/3x4x5 + … + 1/2018x2019x2020
⇒ 2A = 2/1x2x3 + 2/2x3x4 + 2/3x4x5 + … + 2/2018x2019x2020
⇒ 2A= -1/1×2 + 1/2×3 – 1/2×3 +1/3×4 – 1/3×4 + 1/4×5 + … -1/2018×2019 + 1/2019×2020
⇒ 2A = -1/1×2 + 1/2019×2020
A = 2039189/4078380