Question

\(\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+...............+\frac{3}{602\cdot605}\)

Answer 1

Đặt \(A=\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{602.605}\)

\(A=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{602}-\frac{1}{605}\)

\(A=\frac{1}{5}-\frac{1}{605}\)

\(A=\frac{24}{121}\)

Answer 2

\(\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+...+\frac{3}{602\cdot605}\)

\(=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{602}-\frac{1}{605}\)

\(=\frac{1}{5}-\frac{1}{605}+0+...+0\)

\(=\frac{24}{121}\)

Answer 3

\(=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{602}-\frac{1}{605}\)

\(=\frac{1}{5}-\frac{1}{605}\)

Answer 4

Ta có:

\(\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{602.605}\)

\(=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}++....+\frac{1}{602}-\frac{1}{605}\)

\(=\frac{1}{5}-\frac{1}{605}=\frac{604}{121}\)

Vậy giá trị biểu thức là \(\frac{604}{121}\)

Answer 5

\(=\frac{1}{5}-\frac{1}{8}+...+\frac{1}{602}-\frac{1}{605}\)

\(=\frac{1}{5}-\frac{1}{605}\)

\(=\frac{24}{121}\)

Answer 6

\(\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+....+\frac{3}{602\cdot605}\)

\(=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+....+\frac{1}{602}-\frac{1}{605}\)

\(=\frac{1}{5}-\frac{1}{605}\)

\(=\frac{24}{121}\)

Answer 7

Ta có:\(\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{602.605}\)

Phân tích:

\(\frac{3}{5.8}=\frac{3}{5}-\frac{3}{8}\) = \(\frac{1}{5}-\frac{1}{8}\)

\(\frac{3}{8.11}=\frac{3}{8}-\frac{3}{11}\)=\(\frac{1}{8}-\frac{1}{11}\)

...

\(\frac{3}{602.605}=\frac{3}{602}-\frac{3}{605}\)=\(\frac{1}{602}-\frac{1}{605}\)

Ta được: \(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{602}-\frac{1}{605}\)

= \(\frac{1}{5}-\frac{1}{605}\)

= \(\frac{24}{121}\)