\(\frac{1}{6}\) + \(\frac{2}{15}\) + \(\frac{3}{40}\) + \(\frac{4}{96}\) + \(\frac{5}{204}\)

= \(\frac{3}{10}\)+\(\frac{3}{40}\)+ \(\frac{4}{96}\) + \(\frac{5}{204}\)

=\(\frac{3}{8}\)+\(\frac{4}{96}\)+ \(\frac{5}{204}\)

= \(\frac{5}{12}\)+ \(\frac{5}{204}\)

Hok tốt !

k nha <3

= \(\frac{15}{34}\)

=1/2x3+2/3x5+3/5x8+4/8x12+5/12x17+6/17x23+7/23x30

=1/2-1/3+1/3-1/5+...+1/23-1/30

=1/2-1/30

=7/15

(2/ 3. 5 + 3/ 5. 8 + 4/ 8. 12 + 5/ 12. 17+ 6/ 17. 23). x(x- 1)= 20/ 69

(1/ 3-1/ 5 + 1/ 5-1/ 8 + 1/ 8-1/ 12 + 1/ 12-1/ 17+ 1/ 17-1/ 23). x(x- 1)= 20/ 69

(1/ 3-1/ 23). x(x- 1)= 20/ 69

mk làm đến đâu còn lại bạn tự làm nha

\(A=\frac{3-2}{2\times3}+\frac{5-3}{3\times5}+\frac{8-5}{5\times8}+...\frac{38-30}{30\times38}+\frac{47-38}{38\times47}\)

\(A=\frac{3}{2\times3}-\frac{2}{2\times3}+\frac{5}{3\times5}-\frac{3}{3\times5}+...\frac{38}{30\times38}-\frac{30}{30\times38}+\frac{47}{38\times47}-\frac{38}{38\times47}\)

\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}+...+\frac{1}{30}-\frac{1}{38}+\frac{1}{38}-\frac{1}{47}\)

\(A=\frac{1}{2}-\frac{1}{47}=\frac{47}{94}-\frac{2}{94}=\frac{45}{94}\)

Lời giải:

Tổng 10 phân số đầu tiên là:
$\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{4}{96}+\frac{5}{204}+.....+\frac{10}{2679}$

$=\frac{1}{2.3}+\frac{2}{3.5}+\frac{3}{5.8}+\frac{5}{8.12}+\frac{5}{12.17}+\frac{6}{17.23}+\frac{7}{23.30}+\frac{8}{30.38}+\frac{9}{38.47}+\frac{10}{47.57}$

$=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{47}-\frac{1}{57}$

$=\frac{1}{2}-\frac{1}{57}=\frac{55}{114}$

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a) Ta có B = \(\left(\frac{2}{15}+\frac{3}{40}+\frac{4}{96}+\frac{5}{204}+\frac{6}{391}\right).x.\left(x-1\right)=\frac{20}{69}\)

         => \(\left(\frac{2}{3.5}+\frac{3}{5.8}+\frac{4}{8.12}+\frac{5}{12.17}+\frac{6}{17.23}\right).x.\left(x-1\right)=\frac{20}{69}\)

         => \(\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{12}+\frac{1}{12}-\frac{1}{17}+\frac{1}{17}-\frac{1}{23}\right).x.\left(x-1\right)=\frac{20}{69}\)

        => \(\left(\frac{1}{3}-\frac{1}{23}\right).x.\left(x-1\right)=\frac{20}{69}\)

        => \(\frac{20}{69}.x.\left(x-1\right)=\frac{20}{69}\)

       => \(x.\left(x-1\right)=\frac{20}{69}:\frac{20}{69}\)

      => \(x.\left(x-1\right)=1\)

      => \(x\in\varnothing\) 

a)  \(\left(\frac{1}{4}+\frac{1}{28}+\frac{1}{70}+....+\frac{1}{8554}\right).x=\frac{31}{94}\)

=> \(\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{91.94}\right).x=\frac{31}{94}\) 

=> \(\frac{1}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{91.94}\right)=\frac{31}{94}\)

=> \(\frac{1}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{91}-\frac{1}{94}\right).x=\frac{31}{94}\)

=> \(\frac{1}{3}.\left(1-\frac{1}{94}\right).x=\frac{31}{94}\)

=> \(\frac{1}{3}.\frac{93}{94}.x=\frac{31}{94}\)

=> \(\frac{31}{94}.x=\frac{31}{94}\)

=> \(x=\frac{31}{94}:\frac{31}{94}\)

=> \(x=1\)

khó thế toy ko bt =)))

toy cũng vậy

mn đừng trả lời nhé

tại sao không

\(\frac{1}{6}\)+\(\frac{2}{15}\)+\(\frac{3}{40}\)+\(\frac{4}{96}\)\(\frac{5}{204}\)

=\(\frac{1}{2x3}\)+\(\frac{2}{3x5}\)+\(\frac{3}{5x8}\)+\(\frac{4}{8x12}\)\(\frac{5}{12x17}\)

=\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{8}\)+\(\frac{1}{8}\)-\(\frac{1}{12}\)+\(\frac{1}{12}\)-\(\frac{1}{17}\)

=\(\frac{1}{2}\)+(\(\frac{1}{3}\)-\(\frac{1}{3}\))+(\(\frac{1}{5}\)-\(\frac{1}{5}\))+(\(\frac{1}{8}\)-\(\frac{1}{8}\))+(\(\frac{1}{12}\)-\(\frac{1}{12}\))-\(\frac{1}{17}\)

=\(\frac{1}{2}\)-\(\frac{1}{17}\)

=\(\frac{15}{34}\)

mn ủng hộ nhé

\(\dfrac{3}{4}-\left[\left(-\dfrac{3}{5}\right)-\left(\dfrac{1}{12}+\dfrac{2}{4}\right)\right]\\ =\dfrac{3}{4}-\left[\left(-\dfrac{3}{5}\right)-\left(\dfrac{1}{12}+\dfrac{6}{12}\right)\right]\\ =\dfrac{3}{4}-\left[\left(-\dfrac{3}{5}\right)-\dfrac{7}{12}\right]\\ =\dfrac{3}{4}-\left[\left(-\dfrac{36}{60}\right)-\dfrac{35}{60}\right]\\ =\dfrac{3}{4}-\left(-\dfrac{71}{60}\right)\\ =\dfrac{3}{4}+\dfrac{71}{60}\\ =\dfrac{35}{60}+\dfrac{71}{60}\\ =\dfrac{106}{60}\\ =\dfrac{53}{30}\)

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\(-\dfrac{6}{7}.\dfrac{21}{12}\\ =-\dfrac{126}{84}\\ =-\dfrac{63}{42}\\ =-\dfrac{31}{14}\)

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\(\left(-5\right).\left(-\dfrac{6}{20}\right)\\ =\dfrac{\left(-5\right).\left(-6\right)}{20}\\ =\dfrac{30}{20}\\ =\dfrac{3}{2}\)

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\(-\dfrac{31}{36}:\left(-\dfrac{37}{72}\right)\\ =-\dfrac{31}{36}.\left(-\dfrac{72}{37}\right)\\ =\dfrac{2322}{1332}\)

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\(\left(-\dfrac{5}{17}\right):\left(-15\right)\\ =\left(-\dfrac{5}{17}\right).\left(-\dfrac{1}{15}\right)\\ =\dfrac{5}{255}\\ =\dfrac{1}{51}\)

\(\dfrac{3}{4}-\left[\left(-\dfrac{3}{5}\right)-\left(\dfrac{1}{12}+\dfrac{2}{4}\right)\right]\\ =\dfrac{3}{4}-\left[\left(-\dfrac{3}{5}\right)-\left(\dfrac{1}{12}+\dfrac{6}{12}\right)\right]\\ =\dfrac{3}{4}-\left[\left(-\dfrac{3}{5}\right)-\dfrac{7}{12}\right]\\ =\dfrac{3}{4}-\left[\left(-\dfrac{36}{60}\right)-\dfrac{35}{60}\right]\\ =\dfrac{3}{4}-\left(-\dfrac{71}{60}\right)\\ =\dfrac{3}{4}+\dfrac{71}{60}\\ =\dfrac{35}{60}+\dfrac{71}{60}\\ =\dfrac{106}{60}\\ =\dfrac{53}{30}\)

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\(-\dfrac{6}{7}.\dfrac{21}{12}\\ =-\dfrac{126}{84}\\ =-\dfrac{63}{42}\\ =-\dfrac{31}{14}\)

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\(\left(-5\right).\left(-\dfrac{6}{20}\right)\\ =\dfrac{\left(-5\right).\left(-6\right)}{20}\\ =\dfrac{30}{20}\\ =\dfrac{3}{2}\)

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