\(A = \frac{1}{1 \times 2 \times 3} + \frac{1}{2 \times 3 \times 4} + \frac{1}{3 \times 4 \times 5} + \dots + \frac{1}{28 \times 29 \times 30}\)

\(\Rightarrow2A=\frac{2}{1 \times2 \times3}+\frac{2}{2 \times3 \times4}+\frac{2}{3 \times4 \times5}+\dots+\frac{2}{28 \times29 \times30}\)

\(2A = \frac{3 - 1}{1 \times 2 \times 3} + \frac{4 - 2}{2 \times 3 \times 4} + \frac{5 - 3}{3 \times 4 \times 5} + \dots + \frac{30 - 28}{28 \times 29 \times 30}\)

\(2A = \left( \frac{1}{1 \times 2} - \frac{1}{2 \times 3} \right) + \left( \frac{1}{2 \times 3} - \frac{1}{3 \times 4} \right) + \left( \frac{1}{3 \times 4} - \frac{1}{4 \times 5} \right) + \dots + \left( \frac{1}{28 \times 29} - \frac{1}{29 \times 30} \right)\)

\(2A=\frac{1}{1 \times2}-\frac{1}{29 \times30}=\frac{1}{2}-\frac{1}{870}\)

\(2A=\frac{434}{870}\Rightarrow A=\frac{434}{870}:2=\frac{217}{870}\)

Fe + 2HCl → FeCl2 + H2

BAI 1;

1. tom runs faster than peter

2. lan does her homework more carefully than mai

3. nam speaks english more fluently than minh

4. john works harder than his brother

5. she sings better than me

6. the old man walks more slowly than the young man

BAI 2:

1. jim's classmates look much older than him

2. my parent's house is bigger than mine

3. the read dress is cheaper than the black one

4. yesterday was warmer than today

5. i dont think i'm shorter than you

6. is john better at math than jim?

BAI 3:

1. faster

2. more beautifully

3. harder

4. more fluently

5. carefully

6. better

BAI 1;

1. tom runs faster than peter

2. lan does her homework more carefully than mai

3. nam speaks english more fluently than minh

4. john works harder than his brother

5. she sings better than me

6. the old man walks more slowly than the young man

BAI 2:

1. jim's classmates look much older than him

2. my parent's house is bigger than mine

3. the read dress is cheaper than the black one

4. yesterday was warmer than today

5. i dont think i'm shorter than you

6. is john better at math than jim?

BAI 3:

1. faster

2. more beautifully

3. harder

4. more fluently

5. carefully

6. better

tốc độ là đại lượng vô hướng, có giá trị lớn hơn hoặc bằng 0

còn vận tốc là đại lượng vector, giá trị có thể âm, dương hoặc bằng 0

đặt \(S = \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots + \frac{1}{3^{2021}}\)

\(\Rightarrow3\times S=3\times\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\dots+\frac{1}{3^{2021}}\right)\) (1)

\(\Rightarrow3\times S=1+\frac{1}{3}+\frac{1}{9}+\dots+\frac{1}{3^{2020}}\) (2)

lấy (2) trừ (1) ta được:

\(3 \times S - S = \left(1 + \frac{1}{3} + \frac{1}{9} + \dots + \frac{1}{3^{2020}}\right) - \left(\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots + \frac{1}{3^{2021}}\right)\)

\(\Rightarrow2\times S=1-\frac{1}{3^{2021}}\)

\(\Rightarrow S=\left(1-\frac{1}{3^{2021}}\right):2\Rightarrow S=\frac{1}{2}-\frac{1}{2 \times3^{2021}}\)

\(a.\frac{-1}{12}+\frac{4}{3}=\frac{-1}{12}+\frac{16}{12}=\frac{15}{12}=\frac{5}{4}\)

\(b.\left(\frac{-4}{14}-\frac{3}{15}\right)-\left(\frac{1}{5}-\frac{20}{35}-(-1)\right)\cdot7\)

\(= \left(\frac{-2}{7} - \frac{1}{5}\right) - \left(\frac{1}{5} - \frac{4}{7} + 1\right) \cdot 7\)

\(=\frac{-17}{35}-\frac{23}{35}\cdot7=\frac{-17}{35}-\frac{23}{5}=\frac{-178}{35}\)

\(c.\frac{3}{5}+\frac{-5}{20}+\frac{30}{75}+\frac{-7}{4}=\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{-1}{4}+\frac{-7}{4}\right)\)

\(= 1 + (-2) = -1\)

\(d.\frac{5}{6}\cdot\left(\frac{-12}{13}\right)+\frac{7}{13}=\frac{-10}{13}+\frac{7}{13}=\frac{-3}{13}\)

\(e.\frac{2}{-9}-\frac{5}{-36}-\frac{1}{4}=\frac{-2}{9}+\frac{5}{36}-\frac{1}{4}\)

\(=\frac{-8}{36}+\frac{5}{36}-\frac{9}{36}=\frac{-12}{36}=\frac{-1}{3}\)

\(f.\frac{2}{23}+\frac{-5}{12}+\frac{7}{18}+\frac{21}{23}+\frac{-7}{12}\)

\(= \left(\frac{2}{23} + \frac{21}{23}\right) + \left(\frac{-5}{12} + \frac{-7}{12}\right) + \frac{7}{18}\)

\(= 1 + (-1) + \frac{7}{18} = \frac{7}{18}\)