\(\frac{3}{10}+\frac{3}{40}+\frac{3}{88}+...+\frac{3}{340}\)

\(=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{17.20}\)

\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\)

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

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

\(\frac{3}{10}+\frac{3}{40}+\frac{3}{88}+...+\frac{3}{340}\)

\(=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{17.20}\)

\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\)

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

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

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

\(\frac{7}{1.3}+\frac{7}{3.5}+\frac{7}{5.7}+...+\frac{7}{99.101}\)

\(=\frac{7}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)

\(=\frac{7}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=\frac{7}{2}.\left(1-\frac{1}{101}\right)\)

\(=\frac{7}{2}.\frac{100}{101}\)

\(=\frac{7}{5050}\)

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.101}\)

\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{101}\right)\)

\(=\frac{1}{2}.\frac{100}{101}\)

\(=\frac{1}{5050}\)

\(\frac{2}{1.3}\)+\(\frac{2}{3.5}\)+...+\(\frac{2}{99.101}\)
=1-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{5}\)+...+\(\frac{1}{99}\)-\(\frac{1}{100}\)

=1-\(\frac{1}{100}\)=\(\frac{99}{100}\)

     \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)

\(=1-\frac{1}{101}\)

\(=\frac{100}{101}\)

11¹⁹⁷⁹ > 32¹³²⁰

1 . Tìm phân số bằng 5/7 biết :

a, Tổng của tử và mẫu là 144

Phân số đó là:\(\frac{60}{84}\)

b, Hiệu của tử và mẫu là 30

Phân số đó là:​ \(\frac{75}{105}\)

c, Tích của tử và mẫu là 3500

Phân số đó là:​ \(\frac{50}{70}\)

ta có 

\(a.\frac{x}{y}=\frac{5}{7}\Leftrightarrow\frac{x}{x+y}=\frac{5}{5+7}\Leftrightarrow\frac{x}{144}=\frac{5}{12}\Leftrightarrow x=60\Rightarrow y=84\) và \(\frac{x}{y}=\frac{60}{84}\)

\(b.\frac{x}{y}=\frac{5}{7}\Leftrightarrow\frac{x}{y-x}=\frac{5}{7-5}\Leftrightarrow\frac{x}{30}=\frac{5}{2}\Leftrightarrow x=75\Rightarrow y=105\) vậy \(\frac{x}{y}=\frac{75}{105}\)

c. \(\frac{x}{y}=\frac{5}{7}\Leftrightarrow\frac{x^2}{xy}=\frac{5}{7}\Leftrightarrow\frac{x^2}{3500}=\frac{5}{7}\Leftrightarrow x^2=2500\Rightarrow x=50\Rightarrow y=70\Rightarrow\frac{x}{y}=\frac{50}{70}\)

x và y có là các số nguyên không?

Phức tạp lắm!

\(\frac{2}{5}+x=\frac{-11}{15}\)

\(x=\frac{-11}{15}-\frac{2}{5}\)

\(x=\frac{-11}{15}-\frac{6}{15}\)

\(x=\frac{-17}{15}\)

\(\frac{2}{5}+x=\frac{-11}{15}\)

            \(x=\frac{-11}{15}-\frac{2}{5}\)

            \(x=\frac{-11}{15}-\frac{6}{15}\)

            \(x=\frac{-17}{15}\)

Vậy \(x=\frac{-17}{15}\)

115−15(6𝑥−23)=25

115−90𝑥+345=25

460−90𝑥=25

−90𝑥+460=25

−90𝑥=−435

𝑥=29/6

Trả lời:

115 - 15 ( 6x - 23 ) = 25

=> 15 ( 6x - 23 ) = 115 - 25

=> 15 ( 6x - 23 ) = 90

=> 6x - 23 = 90 : 15

=> 6x - 23 = 6

=> 6x = 6 + 23

=> 6x = 29

=> x = 29/6

Vậy x = 29/6