\(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}\)

\(=\)\(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20}\)

\(=\frac{1}{2}-\frac{1}{20}\)

\(=\frac{10}{20}-\frac{1}{20}\)

\(=\frac{9}{20}\)

Tk giúp !!

\(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}\)

\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}\)

\(=\frac{1}{2}-\frac{1}{14}\)

\(=\frac{7}{14}-\frac{1}{14}=\frac{6}{14}=\frac{3}{7}\)

\(=3.\left(\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{602}-\frac{1}{605}\right)\right)\)

\(=3.\left(\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{605}\right)\right)\)

\(=3.\left(\frac{1}{2}.\frac{24}{121}\right)\)

\(=3.\frac{24}{242}=3.\frac{12}{121}\)

\(=\frac{36}{121}\)

                    Đáp số :\(\frac{36}{121}\)

Các bạn ơi ủng hộ mik nhé cảm ơn các bạn rất rất rất nhiều! ^_^

a: \(=3\cdot\dfrac{6+14-9}{42}\cdot\dfrac{14}{11}\)

\(=3\cdot\dfrac{11}{42}\cdot\dfrac{14}{11}=1\)

b: \(=\dfrac{19}{5}\cdot\dfrac{11}{10}+\dfrac{9}{5}\cdot\dfrac{7}{3}\)

\(=\dfrac{209}{50}+\dfrac{63}{15}=4.18+4.2=8,38\)

b: \(27D=3^{14}+3^{17}+...+3^{2024}\)

\(\Leftrightarrow26D=3^{2024}-3^{11}\)

hay \(D=\dfrac{3^{2024}-3^{11}}{26}\)

c: \(25E=-5^4-5^6-...-5^{1002}\)

\(\Leftrightarrow24E=-5^{1002}+5^2\)

hay \(E=\dfrac{-5^{1002}+5^2}{24}\)

Phương pháp giải:

Tính nhẩm các số rồi điền kết quả vào chỗ trống.

Lời giải chi tiết:

Tính nhẩm:

=(3/10/99+4/11/119-5/8/299)*(3/6-2/6-1/6)

=(3/10/99+4/11/119-5/8/299)*(1/6-1/6)

=(3/10/99+4/11/119-5/8/299)*0

=0