\(\frac{1}{2\times5}+\frac{1}{5\times8}+\frac{1}{8\times11}+\frac{1}{11\times14}+\frac{1}{14\times17}+\frac{1}{17\times20}\)

\(=\frac{1}{3}\times\left(\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+\frac{3}{14\times17}+\frac{3}{17\times20}\right)\)

\(=\frac{1}{3}\times\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\right)\)

\(=\frac{1}{3}\times\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(=\frac{1}{3}\times\frac{9}{20}\)

\(=\frac{3}{20}\)

_Chúc bạn học tốt_

Đặt \(A=\frac{1}{2x5}+\frac{1}{5x8}+..+\frac{1}{17x20}\)

\(3xA=3x\left(\frac{1}{2x5}+\frac{1}{5x8}+...+\frac{1}{17x20}\right)\)

\(3xA=\frac{3}{2x5}+\frac{3}{5x8}+....+\frac{3}{17x20}\)

\(3xA=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+..+\frac{1}{17}-\frac{1}{20}\)

\(3xA=\frac{1}{2}-\frac{1}{20}\)

\(3xA=\frac{9}{20}\)

\(\Rightarrow A=\frac{3}{20}\)

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

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

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

\(=\frac{6}{14}\)

\(=\frac{3}{7}\)

3/2x5 + 3/5x8 + 3/8x11 + 3/11x14 

= 3/2 - 3/5 + 3/5 - 3/8 + 3/8 - 3/11 + 3/11 - 3/14 

= 3/2 - 3/14 

= 21/14 - 3/14 

= 18/14 

= 9/5 

\(B=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}=\frac{1}{2}-\frac{1}{14}=\frac{3}{7}\)

= 2 x ( 1/2 x 5 + 1/ 5 x 8 + 1/ 8 x 11 + 1/ 11 x 14 + 1/ 14 x 17 )

= 2 x ( 1/2 - 1/5 + 1/5 - 1/8 + ....+1/14 - 1/17)

= 2 x (1/2 - 1/17)

= 2 x 15/34

= 15/17

ĐÚNG THÌ TÍCH CHO MÌNH NHA

CHÚC BẠN HỌC GIỎI

Đặt \(A=\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}\)

\(A=\frac{2}{3}\cdot\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{17}\right)\)

\(A=\frac{2}{3}\cdot\left(\frac{1}{2}-\frac{1}{17}\right)\)

\(A=\frac{2}{3}\cdot\frac{15}{34}=\frac{5}{17}\Rightarrow A< 1\)

   \(\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}\)

\(=\frac{2}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}\right)\)

\(=\frac{2}{3}.\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\right)\)

\(=\frac{2}{3}.\left(1-\frac{1}{17}\right)\)

\(=\frac{2}{3}.\frac{16}{17}\)

\(=\frac{32}{51}< \frac{51}{51}=1\)

\(\Rightarrow\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}< 1\)

toán 6 hả

X3 lên nhé

X3 lên

nhân cả tử và mẫu cho 3 là làm đc thôi

Giải:

Ta có:

\(\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+...+\frac{3}{\left(x-3\right)\times x}=\frac{1}{6}\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{x-3}-\frac{1}{x}=\frac{1}{6}\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{x}=\frac{1}{6}\)

\(\Leftrightarrow\frac{1}{x}=\frac{1}{2}-\frac{1}{6}=\frac{1}{3}\Leftrightarrow x=3\)

De thoi ma,minh ko ghi lai de nha

=\(\frac{1}{2}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{8}\)+...+...=\(\frac{1}{6}\)

=\(\frac{1}{2}\)-\(\frac{1}{x}\)=\(\frac{1}{6}\)

Con lai bn tu lam nha . chuc bn hok tot !!!

\(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+....+\frac{3}{\left(x-3\right).x}=\frac{1}{6}\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+....+\frac{1}{\left(x-3\right)}-\frac{1}{x}=\frac{1}{6}\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{x}=\frac{1}{6}\)

\(\Leftrightarrow\frac{1}{x}=\frac{1}{2}-\frac{1}{6}\)

\(\Leftrightarrow\frac{1}{x}=\frac{1}{3}\)

\(\Leftrightarrow x=1\div\frac{1}{3}=3\)

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585u7=35o0e3iu

ta co 01234

lên mạng mà tra

\(P=\frac{1}{5x8}+\frac{1}{8x11}+.....+\frac{1}{602x605}\)

\(\Rightarrow3P=\frac{3}{5x8}+\frac{3}{8x11}+......+\frac{3}{602x605}\)

\(\Rightarrow3P=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-.....+\frac{1}{602}-\frac{1}{605}\)

\(\Rightarrow3P=\frac{1}{5}-\frac{1}{605}\)

\(\Rightarrow3P=\frac{24}{121}\)

\(\Rightarrow P=\frac{24}{121}:3\)

\(\Rightarrow P=\frac{8}{121}\)

\(Q=\frac{4}{3x7}+\frac{5}{7x12}+\frac{1}{12x13}+\frac{7}{13x20}+\frac{3}{20x23}\)

\(Q=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+\frac{1}{13}-\frac{1}{20}+\frac{1}{20}-\frac{1}{23}\)

\(Q=\frac{1}{3}-\frac{1}{23}\)

\(Q=\frac{20}{69}\)

câu 1 = 1/5 -1/8+1/8 -1/11+1/11-1/14+.....+1/602-1/605

bây giờ cậu xoá các phân số gống nhau mà có phép cộng như 1/8+1/8 là xoá tương tự như vậy xoá các phân số bằng dấu gạch các phân số như / thế đó nhé

là xoá hết còn phân số 1/5-1/605 mà trừ là theo kiểu tìm x nhé