tính : 3/1*2*3 + 3/1*2*3 + …………..+3/18*19*20 23/08/2021 Bởi Autumn tính : 3/1*2*3 + 3/1*2*3 + …………..+3/18*19*20
3/1.2.3 + 3/2.3.4 + … + 3/18.19.20 = 3/2 . (2/1.2.3 + 2/2.3.4 + … + 2/18.19.20) = 3/2 . (1/1.2 – 1/2.3 – 1/3.4 + … + 1/18.19 – 1/19.20 = 3/2 . (1/1.2 – 1/19.20) = 3/2 . (1/2 – 1/380) = 3/2 . 189/380 = 567/760 Bình luận
Đáp án: $\dfrac{567}{760}$ Giải thích các bước giải: Sửa lại đề bài: $\dfrac{3}{1.2.3}+\dfrac{3}{2.3.4}+…+\dfrac{3}{18.19.20}$ $\dfrac{3}{1.2.3}+\dfrac{3}{2.3.4}+…+\dfrac{3}{18.19.20}\\=\dfrac{3}{2}\left ( \dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+…+\dfrac{2}{18.19.20} \right )\\=\dfrac{3}{2}\left ( \dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+…+\dfrac{1}{18.19}-\dfrac{1}{19.20} \right )\\=\dfrac{3}{2}\left ( \dfrac{1}{1.2}-\dfrac{1}{19.20} \right )\\=\dfrac{3}{2}\left ( \dfrac{1}{2}-\dfrac{1}{380} \right )\\=\dfrac{3}{2}.\dfrac{189}{380}=\dfrac{567}{760}$ Bình luận
3/1.2.3 + 3/2.3.4 + … + 3/18.19.20
= 3/2 . (2/1.2.3 + 2/2.3.4 + … + 2/18.19.20)
= 3/2 . (1/1.2 – 1/2.3 – 1/3.4 + … + 1/18.19 – 1/19.20
= 3/2 . (1/1.2 – 1/19.20)
= 3/2 . (1/2 – 1/380)
= 3/2 . 189/380
= 567/760
Đáp án: $\dfrac{567}{760}$
Giải thích các bước giải:
Sửa lại đề bài: $\dfrac{3}{1.2.3}+\dfrac{3}{2.3.4}+…+\dfrac{3}{18.19.20}$
$\dfrac{3}{1.2.3}+\dfrac{3}{2.3.4}+…+\dfrac{3}{18.19.20}\\=\dfrac{3}{2}\left ( \dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+…+\dfrac{2}{18.19.20} \right )\\=\dfrac{3}{2}\left ( \dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+…+\dfrac{1}{18.19}-\dfrac{1}{19.20} \right )\\=\dfrac{3}{2}\left ( \dfrac{1}{1.2}-\dfrac{1}{19.20} \right )\\=\dfrac{3}{2}\left ( \dfrac{1}{2}-\dfrac{1}{380} \right )\\=\dfrac{3}{2}.\dfrac{189}{380}=\dfrac{567}{760}$