\(1\frac{13}{15}\cdot3\cdot(0,5)^2\cdot3+\left[\frac{8}{15}-1\frac{19}{60}:1\frac{23}{24}\right]\)

\(=\frac{28}{15}\cdot3\cdot0,5\cdot0,5\cdot3+\left[\frac{8}{15}-\frac{79}{60}:\frac{47}{24}\right]\)

\(=\frac{28}{5}\cdot0,25\cdot3+\left[\frac{32}{60}-\frac{79}{60}\cdot\frac{24}{47}\right]\)

\(=\frac{28}{5}\cdot\frac{25}{100}\cdot3+\left[\frac{32}{60}-\frac{158}{235}\right]\)

\(=\frac{28}{5}\cdot\frac{1}{4}\cdot3+\frac{-98}{705}=\frac{7}{5}\cdot1\cdot3+\frac{-98}{705}\)

Đến đây là tính dễ rồi :v

\((-3,2)\cdot\frac{-15}{64}+\left[0,8-2\frac{4}{15}\right]:1\frac{23}{24}\)

\(=\frac{-32}{10}\cdot\frac{-15}{64}+\left[\frac{8}{10}-\frac{34}{15}\right]:\frac{47}{24}\)

\(=\frac{-32\cdot(-15)}{10\cdot64}+\left[\frac{4}{5}-\frac{34}{15}\right]:\frac{47}{24}\)

\(=\frac{-1\cdot(-3)}{2\cdot2}+\frac{4\cdot3-34}{15}:\frac{47}{24}\)

\(=\frac{3}{4}+\frac{-22}{15}:\frac{47}{24}\)

\(=\frac{3}{4}+\frac{-517}{180}=\frac{-191}{90}\)

Bài 2 : \(\frac{2\cdot(-13)\cdot9\cdot10}{(-3)\cdot4\cdot(-5)\cdot26}=\frac{1\cdot(-1)\cdot3\cdot2}{(-1)\cdot2\cdot(-1)\cdot2}=\frac{1\cdot3}{-1\cdot2}=\frac{3}{-2}=\frac{-3}{2}\)

\(\frac{15\cdot8+15\cdot4}{12\cdot3}=\frac{15\cdot(8+4)}{12\cdot3}=\frac{15\cdot12}{12\cdot3}=\frac{15}{3}=5\)

a)1.2.3.4...9-1.2.3.4...8-1.2.3.4...8.8

=1.2.3.4...8(9-1-8)

=1.2.3.4...8.0

=0

b)(3.4.2¹⁶)²/11.12³.4¹¹-16⁹=(3.2².2¹⁶)²/11.2¹³.2²²-2³⁶=3².2⁴.2³²/11.2³⁵-2³⁶=3².2²⁶/2³⁵.(11-2)

=3².2³⁶/2³⁵.9=3².2³⁶/2³⁵.3²=2

c)70.(131313/565656+131313/727272+131313/909090

=70.(13/56+13/72+13/90)

=70.39/70=39

d)1/4.9+1/9.14+1/14.19+...+1/64.69

=4/4.9.4+4/9.4.14+4/14.19.4+...+4/64.69.4.

=1/4.(4/4.9+4/9.14+4/14.19+...+4/64.69)

=1/4.(1/4-1/9+1/9-1/14+1/14-1/19+...+1/64-1/69)

=1/4.(1/4-1/69)

=1/4.65/276=65/1104

~~~~~~~~Chúc bạn học giỏi nhé !~~~~~~~~

nhìu thế này sao mà làm nổi

d)\(\frac{1}{3}\times\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{64}-\frac{1}{69}\right)\)

\(\frac{1}{3}\times\left(\frac{1}{4}-\frac{1}{69}\right)\)

\(\frac{1}{3}\times\frac{65}{276}\)

A) \(\frac{1}{6}\) = 0,1666666665

B) 0,1666669167

\(\frac{1}{6}\) < \(\frac{111111}{666665}\) 

Bạn lấy tử chia cho mẫu là ra

nhanh lên nhé

(1+\(\frac{1}{3}\)) x (1+\(\frac{1}{2x4}\)) x(1+\(\frac{1}{3x5}\))x(1+\(\frac{1}{4x6}\)) x .....x (1+ \(\frac{1}{2009x2011}\))

= \(\frac{2}{1x3}\)x \(\frac{2}{2x4}\)x \(\frac{2}{3x5}\)x \(\frac{2}{4x6}\)x....x \(\frac{2}{2009x2011}\)

= ..................

đến đây tự làm nhé

làm hết đi mà

\(=\frac{47}{6}\)

Ta thấy :

1/1x2 = 1/1 - 1/2

1/2x3 = 1/2 - 1/3 

....

=>( 1/1x2 + 1/2x3 + 1/3x4 + 1/5x6 ) x 10 - x = ( 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 ) x 10 - x

= ( 1/1 - 1/6 ) x 10 - x =0

 5/6 x 10 - x = 0 

 25/3 - x = 0

=> x = 25/3

\(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{5.6}\right).10-x=0\)

\(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{30}\right).10-x=0\)

\(\left(1-\frac{1}{4}+\frac{1}{30}\right).10-x=0\)

\(\left(\frac{3}{4}+\frac{1}{30}\right).10-x=0\)

\(\frac{47}{60}.10-x=0\)

\(\frac{47}{6}-x=0\)

\(x=\frac{47}{6}-0\)

\(x=\frac{47}{6}\)