Bài 1:

a, 3\(\dfrac{2}{5}\) - \(\dfrac{1}{2}\) 

= \(\dfrac{17}{5}\) - \(\dfrac{1}{2}\) 

= \(\dfrac{34}{10}\) - \(\dfrac{5}{10}\)

= \(\dfrac{29}{10}\)

b, \(\dfrac{4}{5}\) + \(\dfrac{1}{5}\) x \(\dfrac{3}{4}\)

= \(\dfrac{4\times4}{5\times4}\) + \(\dfrac{1\times3}{5\times4}\)

= \(\dfrac{16}{20}\) + \(\dfrac{3}{20}\)

= \(\dfrac{19}{20}\)

c, 4\(\dfrac{4}{9}\) : 2\(\dfrac{2}{3}\) + 3\(\dfrac{1}{6}\)

= \(\dfrac{40}{9}\) : \(\dfrac{8}{3}\) + \(\dfrac{19}{6}\)

= \(\dfrac{5}{3}\) + \(\dfrac{19}{6}\)

= \(\dfrac{10}{6}\) + \(\dfrac{19}{6}\)

= \(\dfrac{29}{6}\)

Bài 2:

   3\(\dfrac{2}{5}\) + 2\(\dfrac{1}{5}\) 

= \(\dfrac{17}{5}\) + \(\dfrac{11}{5}\)

= \(\dfrac{28}{5}\)

b, 7\(\dfrac{1}{6}\) : 5\(\dfrac{2}{3}\)

= \(\dfrac{43}{6}\) : \(\dfrac{17}{3}\)

= \(\dfrac{43}{34}\)

Bài 3:

a, 800 kg 5g > 8,005 kg

b, 9 ha 4 dam² < 9\(\dfrac{5}{100}\) ha

c, 5m 5mm > 5,0005 m

d, 250 kg > \(\dfrac{1}{5}\) tấn

\(\dfrac{5}{12}+\dfrac{1}{6}=\dfrac{5}{12}+\dfrac{2}{12}=\dfrac{5+2}{12}=\dfrac{7}{12}\)

\(\dfrac{5}{12}+\dfrac{1}{6}=\dfrac{5}{12}+\dfrac{2}{12}=\dfrac{7}{12}\)

\(1-\dfrac{23}{47}=\dfrac{47}{47}-\dfrac{23}{47}=\dfrac{24}{47}\)

\(\dfrac{4}{5}x\dfrac{7}{8}=\dfrac{4x7}{5x8}=\dfrac{28}{40}=\dfrac{7}{10}\)

\(\dfrac{8}{5}:\dfrac{1}{4}=\dfrac{8}{5}x\dfrac{4}{1}=\dfrac{32}{5}\)

\(\dfrac{8}{5}:\dfrac{1}{4}=\dfrac{8}{5}\times4=\dfrac{32}{5}\)

\(\dfrac{4}{5}\times\dfrac{7}{8}=\dfrac{4\times7}{5\times8}=\dfrac{28}{40}=\dfrac{14}{20}=\dfrac{7}{10}\)

A = \(\dfrac{1+5+5^2+5^3+5^4+...+5^{17}}{1+5^2+5^4+...+5^{16}}\)

Đặt tử số là B = 1 + 5 + 5² + 5³ + 5⁴ +...+ 5¹⁷

                  5B =       5 + 5² + 5³ + 5⁴ +...+ 5¹⁷ + 5¹⁸

                  5B - B = 5¹⁸ - 1

                  4B       = 5¹⁸ - 1

                    B       = (5¹⁸ - 1) : 4

Đặt mẫu số là C  = 1 + 5² + 5⁴ +...+ 5¹⁶

                    5².C =       5² + 5⁴ +...+ 5¹⁶ + 5¹⁸

                    25.C - C  =  5¹⁸ - 1

                    24C         =   5¹⁸ - 1

                        C         =    (5¹⁸ - 1): 24 

A = \(\dfrac{B}{C}\) = \(\dfrac{\dfrac{5^{18}-1}{4}}{\dfrac{5^{18}-1}{24}}\)

A = 6 

a=6 banj nha

S = 1/5 + 1/5² + 1/5³ + ... + 1/5¹⁰⁰

⇒ 5S = 1 + 1/5 + 1/5² + ... + 1/5⁹⁹

⇒ 4S = 5S - S

= (1 + 1/5 + 1/5² + ... + 1/5⁹⁹) - (1/5 + 1/5² + 1/5³ + ... + 1/5¹⁰⁰)

= 1 - 1/5¹⁰⁰

⇒ S = (1 - 1/5¹⁰⁰)/4

        S =           \(\dfrac{1}{5}\) + \(\dfrac{1}{5^2}\) + \(\dfrac{1}{5^3}\)+...+\(\dfrac{1}{5^{99}}\)+ \(\dfrac{1}{5^{100}}\)

      5S =     1 + \(\dfrac{1}{5}\) + \(\dfrac{1}{5^2}\) +  \(\dfrac{1}{5^3}\)+...+ \(\dfrac{1}{5^{99}}\)

5S - S =     1 - \(\dfrac{1}{5^{100}}\)

   4S   =       \(\dfrac{5^{100}-1}{4.5^{100}}\)

5 - 1 - 1 = 3     4 - 1 - 1 = 2     3 - 1 - 1 = 1

5 - 1 - 2 = 2     5 - 2 - 1 = 2     5 - 2 - 2 = 1

Lời giải chi tiết:

a. 

\(\left(1\frac{1}{4}+\frac{3}{5}\right):\left(-\frac{11}{12}\right)+\left(\frac{3}{8}-1\frac{2}{5}\right):\left(-\frac{11}{12}\right)\) 

\(=\left(\frac{5}{4}+\frac{3}{5}+\frac{3}{8}-\frac{7}{5}\right):\left(-\frac{11}{12}\right)\)  

\(=\left(\frac{13}{8}-\frac{4}{5}\right):\left(-\frac{11}{12}\right)\) 

\(=\frac{33}{40}:\left(-\frac{11}{12}\right)\) 

\(=\frac{33}{40}\cdot\left(-\frac{12}{11}\right)\) 

\(=\frac{-9}{10}\)  

b. 

\(\left(\frac{3}{8}-1\frac{2}{5}\right):\left(-\frac{11}{15}\right)+\left(1\frac{1}{4}+\frac{3}{5}\right):\left(-\frac{11}{15}\right)\) 

\(=\left(\frac{3}{8}-\frac{7}{5}+\frac{5}{4}+\frac{3}{5}\right):\left(-\frac{11}{15}\right)\)  

\(=\left(\frac{13}{8}-\frac{4}{5}\right):\left(-\frac{11}{15}\right)\) 

\(=\frac{33}{40}:\left(-\frac{11}{15}\right)\) 

\(=\frac{33}{40}\cdot\left(-\frac{15}{11}\right)\) 

\(=\frac{-9}{8}\)