(1 - 1/2) x (1 - 1/3) x (1 - 1/4) x (1 - 1/5)

=1/2 x 2/3 x 3/4 x 4/5

=1/5

\(A=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{18.19.20}\)

\(2A=\dfrac{3-1}{1.2.3}+\dfrac{4-2}{2.3.4}+\dfrac{5-3}{3.4.5}+...+\dfrac{20-18}{18.19.20}=\)

\(=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+...+\dfrac{1}{18.19}-\dfrac{1}{19.20}=\dfrac{1}{2}-\dfrac{1}{19.20}\)

\(\Rightarrow A=\left(\dfrac{1}{2}-\dfrac{1}{19.20}\right):2\)

À quên mọi người tính nhanh nhé !

a) \(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}\)

\(=1-\frac{1}{4}\)

\(=\frac{3}{4}\)

b) \(\frac{4}{7}\times\frac{8}{9}+\frac{4}{7}\times\frac{1}{9}\)

\(=\frac{4}{7}\times\left(\frac{8}{9}+\frac{1}{9}\right)\)

\(=\frac{4}{7}\times1\)

\(=\frac{4}{7}\)

c) \(\frac{13}{6}\times\frac{3}{8}-\frac{3}{8}\times\frac{7}{6}\)

\(=\frac{3}{8}\times\left(\frac{13}{6}-\frac{7}{6}\right)\)

\(=\frac{3}{8}\times1\)

\(=\frac{3}{8}\)

d) \(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+...+\frac{1}{9x10}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

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

\(=\frac{9}{10}\)

a) Bạn tự làm :V

b) \(\frac{4}{7}\times\frac{8}{9}+\frac{4}{7}\times\frac{1}{9}\)

\(=\frac{4}{7}\times\left(\frac{8}{9}+\frac{1}{9}\right)\)

\(=\frac{4}{7}\times1\)

\(=\frac{4}{7}\)

c) \(\frac{13}{6}\times\frac{3}{8}-\frac{3}{8}\times\frac{7}{6}\)

\(=\frac{3}{8}\times\left(\frac{13}{6}-\frac{7}{6}\right)\)

\(=\frac{3}{8}\times1\)

\(=\frac{3}{8}\)

d) Bạn tự làm :v

\(\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)...\left(1+\dfrac{1}{10}\right)\\=\dfrac{3}{2}.\dfrac{4}{3}...\dfrac{11}{10}\\ =\dfrac{11}{2}\)

hi cj hà

a) \(\frac{1}{2}\times\frac{12}{13}+\frac{1}{3}\times\frac{12}{13}+\frac{1}{4}\times\frac{12}{13}\)

  = (1/2 + 1/3 + 1/4) x 12/13

  = 13/12 x 12/13

  = 1

b) (1 - 1/2 ) x (1 - 1/3) x (1 - 1/4) x ( 1  - 1/5)

=   1/2 x 2/3 x 3/4 x 4/5

=    1/5

2.4^x - 1 = 128

=> 4^x - 1 = 64

=> x - 1 = 3

=> x = 4

b, 17.4^2 + 83.16 

= 17.16 + 83.16

= 16(17 + 83)

= 16.100

= 1600

c, a^5 . 10^10.a^15

= a^20.10^10

d, 3{65 - [5(4 + 2.3) - 15] : 7}

= 3{65 - [5(4 + 6) - 15] : 7}

= 3{65 - [5.10 - 15] : 7}

= 3{65 - [50 - 15] : 7}

= 3{65 - 35 : 7}

= 3{65 - 5}

= 3.60

= 180

bạn ghi + - x : nhá

a) \(\frac{2}{3}x\times\frac{1}{2}=\frac{1}{10}\Rightarrow\frac{2}{3}x=\frac{1}{5}\Rightarrow x=\frac{3}{10}\)

vvvvvv

2+ x chia 5 = 6