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6 tháng 11 2020

\(\frac{A}{5}=\frac{1}{5^2}+\frac{1}{5^3}+\frac{1}{5^4}+...+\frac{1}{5^{201}}\)

\(A-\frac{A}{5}=\frac{4A}{5}=\frac{1}{5}-\frac{1}{5^{201}}=\frac{5^{200}-1}{5^{201}}\Rightarrow A=\frac{5^{201}-5}{4.5^{201}}\) 

23 tháng 8 2023

\(a,13\dfrac{3}{5}-\left(8\dfrac{3}{5}-4\dfrac{3}{4}\right)\)

\(=\dfrac{68}{5}-\dfrac{43}{5}+\dfrac{19}{4}\)

\(=5+\dfrac{19}{4}\)

\(=\dfrac{20}{4}+\dfrac{19}{4}=\dfrac{39}{4}\)

\(------\)

\(b,11\dfrac{1}{4}-\left(2\dfrac{5}{7}+5\dfrac{1}{4}\right)\)

\(=\dfrac{45}{4}-\dfrac{19}{7}-\dfrac{21}{4}\)

\(=\left(\dfrac{45}{4}-\dfrac{21}{4}\right)-\dfrac{19}{7}\)

\(=6-\dfrac{19}{7}\)

\(=\dfrac{42}{7}-\dfrac{19}{7}=\dfrac{23}{7}\)

18 tháng 5 2018

ta có : (ghi lại đề)

=6+12+18+24+30/3+6+9+12+15

=2*(3/3+6/6+9/9+12/12+15/15)

=2*(1+1+1+1+1)

=2*5=10

chúc main học tốt nhé

23 tháng 8

hi

Ta có: \(A=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)\cdot...\cdot\left(1-\dfrac{1}{9}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot\dfrac{4}{5}\cdot...\cdot\dfrac{8}{9}\)

\(=\dfrac{1}{9}\)

a: Ta có: \(\dfrac{8}{9}-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{72}\right)\)

\(=\dfrac{8}{9}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{3}-...+\dfrac{1}{8}-\dfrac{1}{9}\right)\)

=0

 

18 tháng 9 2021

câu b, đâu ạ?

21 tháng 9 2018

\(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}+\frac{4}{5}-\frac{5}{6}+\frac{6}{7}+\frac{5}{6}-\frac{4}{5}+\frac{3}{4}-\frac{2}{3}+\frac{1}{2}\)

\(=\left(\frac{1}{2}+\frac{1}{2}+\frac{6}{7}\right)+\left(\frac{2}{3}-\frac{2}{3}\right)+\left(\frac{-3}{4}+\frac{3}{4}\right)+\left(\frac{4}{5}-\frac{4}{5}\right)+\left(\frac{-5}{6}+\frac{5}{6}\right)\)

\(=\frac{13}{7}+0+0+0+0\)

\(=\frac{13}{7}\)

21 tháng 9 2018

\(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}+\frac{4}{5}-\frac{5}{6}+\frac{6}{7}+\frac{5}{6}-\frac{4}{5}+\frac{3}{4}-\frac{2}{3}+\frac{1}{2}.\)

\(=\left(\frac{1}{2}+\frac{1}{2}\right)+\left(\frac{2}{3}-\frac{2}{3}\right)-\left(\frac{3}{4}-\frac{3}{4}\right)+\left(\frac{4}{5}-\frac{4}{5}\right)-\left(\frac{5}{6}-\frac{5}{6}\right)+\frac{6}{7}\)

\(=1+0-0+0+\frac{6}{7}\)

\(=1+\frac{6}{7}=1\frac{6}{7}\)

HQ
Hà Quang Minh
Giáo viên
19 tháng 9 2023

a)

\(\begin{array}{l}\frac{{13}}{{23}}.\frac{7}{{11}} + \frac{{10}}{{23}}.\frac{7}{{11}}\\ = \frac{7}{{11}}.\left( {\frac{{13}}{{23}} + \frac{{10}}{{23}}} \right)\\ = \frac{7}{{11}}.\frac{23}{23}\\ = \frac{7}{{11}}.1\\ = \frac{7}{{11}}\end{array}\)                                   

b)

\(\begin{array}{l}\frac{5}{9}.\frac{{23}}{{11}} - \frac{1}{{11}}.\frac{5}{9} + \frac{5}{9}\\ = \frac{5}{9}.\left( {\frac{{23}}{{11}} - \frac{1}{{11}} + 1} \right)\\ = \frac{5}{9}.\left( {2 + 1} \right)\\ = \frac{5}{9}.3 = \frac{5}{3}\end{array}\)

c)

\(\begin{array}{l}\left[ {\left( { - \frac{4}{9} + \frac{3}{5}} \right):\frac{{13}}{{17}}} \right] + \left( {\frac{2}{5} - \frac{5}{9}} \right):\frac{{13}}{{17}}\\ = \left( { - \frac{4}{9} + \frac{3}{5}} \right).\frac{{17}}{{13}} + \left( {\frac{2}{5} - \frac{5}{9}} \right).\frac{{17}}{{13}}\\ = \frac{{17}}{{13}}.\left( { - \frac{4}{9} + \frac{3}{5} + \frac{2}{5} - \frac{5}{9}} \right)\\ = \frac{{17}}{{13}}.\left[ {\left( { - \frac{4}{9} - \frac{5}{9}} \right) + \left( {\frac{3}{5} + \frac{2}{5}} \right)} \right]\\ =\frac{{17}}{{13}}. (\frac{-9}{9}+\frac{5}{5})\\= \frac{{17}}{{13}}.\left( { - 1 + 1} \right)\\ = \frac{{17}}{{13}}.0 = 0\end{array}\)          

d)

\(\begin{array}{l}\frac{3}{{16}}:\left( {\frac{3}{{22}} - \frac{3}{{11}}} \right) + \frac{3}{{16}}:\left( {\frac{1}{{10}} - \frac{2}{5}} \right)\\ = \frac{3}{{16}}:\left( {\frac{3}{{22}} - \frac{6}{{22}}} \right) + \frac{3}{{16}}:\left( {\frac{1}{{10}} - \frac{4}{{10}}} \right)\\ = \frac{3}{{16}}:\frac{{ - 3}}{{22}} + \frac{3}{{16}}:\frac{{ - 3}}{{10}}\\ = \frac{3}{{16}}.\frac{{ - 22}}{3} + \frac{3}{{16}}.\frac{{ - 10}}{3}\\ = \frac{3}{{16}}.\left( {\frac{{ - 22}}{3} + \frac{{ - 10}}{3}} \right)\\ = \frac{3}{{16}}.\frac{{ - 32}}{3}\\ =  - 2\end{array}\)

6 tháng 9 2016

a.(-2/3+3/7) : 4/5 + (-1/3+4/7) : 4/5

= [(-2/3 + 3/7) + (-1/3 + 4/7)] : 4/5

= [(-2/3 + (-1/3) + (3/7 + 4/7)] : 4/5

= [-1 + 1] : 4/5

= 0 : 4/5

= 0   

6 tháng 9 2016

a) \(\left(\frac{-2}{3}+\frac{3}{7}\right).\frac{5}{4}+\left(\frac{-1}{3}+\frac{4}{7}\right).\frac{5}{4}\)

=\(\left(\frac{-2}{3}+\frac{-1}{3}+\frac{3}{7}+\frac{4}{7}\right).\frac{5}{4}\)

\(0.\frac{5}{4}=0\)

b) \(\frac{5}{9}:\left(\frac{1}{11}-\frac{5}{22}+\frac{1}{15}-\frac{2}{3}\right)\)

=\(\frac{5}{9}:\frac{-81}{110}=\frac{-550}{729}\)

21 tháng 10 2023

a) 1/5 - (1/2 + 3/4 ) : 5/2

= 1/5 - ( 1/4 + 3/4 ) : 5/2

=1/5 - 1 : 5/2

= 1/5 - 1 . 2/5

= 1/5 - 2/5

= -1/5

b) 1,5 . (1/3 - 2/3)

=3/2 . ( -1/3)

=-1/2

c) 9/10 . 23/11 - 1/11 . 9/10 + 9/10

= 9/10 . ( 23/11 - 1/11 ) + 9/10

= 9/10 . 1 + 9/10

= 9/10 + 9/10

= 18/10 = 9/5