b)

\(x-2.\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right)=\frac{16}{9}\)

\(x-2\cdot\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)

\(x-2=\frac{16}{9}:\left(\frac{1}{3}-\frac{1}{9}\right)\)

\(x-2=8\)

=> x = 10

a) 

\(A=\frac{1}{2}.\frac{2}{3}\cdot\frac{3}{4}\cdot\cdot\cdot\frac{2013}{2014}\cdot\frac{2014}{2015}\cdot\frac{2015}{2016}\)

\(A=\frac{1}{2016}\)

$A=\dfrac{\left(\dfrac49\right)^2\cdot\left(-\dfrac9{16}\right)\cdot(-1)^{19}}{\left(\dfrac4{25}\right)^2\cdot\left(-\dfrac{25}{144}\right)^2\cdot\left(-\dfrac{49}{144}\right)^2}$

$=\dfrac{\dfrac{16}{81}\cdot\left(-\dfrac9{16}\right)\cdot(-1)}{\dfrac{16}{625}\cdot\dfrac{625}{144^2}\cdot\dfrac{49^2}{144^2}}$

$=\dfrac{\dfrac19}{\dfrac{49^2}{144^4}}$

$=\dfrac19\cdot\dfrac{144^4}{49^2}$

$=\dfrac19\cdot\dfrac{(2^4\cdot3^2)^4}{7^4}$

$=\dfrac19\cdot\dfrac{2^{16}\cdot3^8}{7^4}$

$=\dfrac{2^{16}\cdot3^6}{7^4}$

$=\dfrac{65536\cdot729}{2401}$

$=\dfrac{47775744}{2401}.$

S=\(^{2^{2010}-2^{2009}-2^{2008}-...-2-1}\)

$A=\left(\dfrac14-1\right)\left(\dfrac19-1\right)\left(\dfrac1{16}-1\right)\cdots\left(\dfrac1{100}-1\right)\left(\dfrac1{121}-1\right)$

$=\left(-\dfrac34\right)\left(-\dfrac89\right)\left(-\dfrac{15}{16}\right)\cdots\left(-\dfrac{99}{100}\right)\left(-\dfrac{120}{121}\right)$

$=(-1)^{10}\cdot\dfrac34\cdot\dfrac89\cdot\dfrac{15}{16}\cdots\dfrac{99}{100}\cdot\dfrac{120}{121}$

$=\dfrac34\cdot\dfrac89\cdot\dfrac{15}{16}\cdot\dfrac{24}{25}\cdots\dfrac{99}{100}\cdot\dfrac{120}{121}$

$=\dfrac{3\cdot8\cdot15\cdot24\cdots99\cdot120}{4\cdot9\cdot16\cdot25\cdots100\cdot121}$

$=\dfrac{(1\cdot2\cdot3\cdots10)\,(3\cdot4\cdot5\cdots12)}{(2\cdot3\cdot4\cdots11)^2}$

$=\dfrac{1\cdot12}{2\cdot11}$

$=\dfrac6{11}.$

\(T=\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right)...\left(1-\frac{1}{576}\right).\left(1-\frac{1}{625}\right)\)

\(T=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{575}{576}.\frac{624}{625}\)

\(T=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{23.25}{24.24}.\frac{24.26}{25.25}\)

\(T=\frac{1.2.3...23.24}{2.3.4...24.25}.\frac{3.4.5...25.26}{2.3.4...24.25}\)

\(T=\frac{1}{25}.\frac{26}{2}=\frac{1}{25}.13=\frac{13}{25}\)

\(T=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}......\frac{575}{576}.\frac{624}{625}\)

\(T=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{23.25}{24.24}.\frac{24.26}{25.25}\)

\(T=\frac{1.2.3....24}{2.3.4...25}.\frac{3.4.5....26}{2.3.4....25}=\frac{1}{25}.\frac{26}{2}=\frac{13}{25}\)

=) \(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{255}{256}.x=\frac{108}{7}\)
=) \(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{15.17}{16.16}.x=\frac{108}{7}\)
=) \(\frac{1.2.3.4.....15}{2.3.4.....16}.\frac{3.4.5.....17}{2.3.4.....16}.x=\frac{108}{7}\)
=) \(\frac{1}{16}.\frac{17}{2}.x=\frac{108}{7}\)=) \(\frac{17}{32}.x=\frac{108}{7}\)=) \(x=\frac{108}{7}:\frac{17}{32}\)
=) \(x=\frac{3456}{119}\)

Đề bài sai tjì phải ,bạn ạ

13/25 có cần giải rõ ko cần thì bảo nhắn qua cho

=\(\frac{3}{2^2}x\frac{8}{3^2}x...x\frac{624}{25^2}\)

=\(\frac{1.3x2.4x...x624}{2^2x3^2x...x25^2}\)

=13/25

a) \(\frac{\left(-1\right)}{4}^2+\frac{3}{8}.\left(\frac{-1}{6}\right)-\frac{3}{16}:\left(\frac{-1}{2}\right)=\left(\frac{-1}{4}\right)^2+\left(\frac{-3}{68}\right)-\left(\frac{-3}{8}\right)=\left(\frac{1}{16}\right)+\left(\frac{-3}{68}\right)-\left(\frac{-3}{8}\right)=\frac{5}{272}-\left(\frac{-3}{8}\right)=\frac{107}{272}\)

$\textbf{a)}$

$A=\left(-\dfrac14\right)^2+\dfrac38\cdot\left(-\dfrac16\right)-\dfrac3{16}:\left(-\dfrac12\right)$

$=\dfrac1{16}-\dfrac1{16}+\dfrac38$

$=\dfrac38.$