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

\(A=2^{2010}\left(2^{2009}+2^{2008}+...+2+1\right)\)

Đặt \(\text{A = 1 + 2 + . . . + 2^{2008} + 2^{2009}}\)

\(\text{⇒ 2 A = 2 + 2 2 + . . + 2^{2010}}\)

⇒ \(A=2^{2010}-1\)

⇒ \(A=2^{2010}-\left(2^{2010}-1\right)\)

⇒ \(A=1\)

b) \(B=2072\)

c) \(\dfrac{4949}{19800}\)

Xin lỗi mình không có nhiều thời gian để giải thích trên đây á nên tạm gửi ảnh mình tạo nhé . Học tốt !

ồ, lâu h ms gặp

a,

Dễ thấy \(\dfrac{2005^{2016}+1}{2005^{2017}+1}< 1\)

Áp dụng khi \(\dfrac{a}{b}< 1\Rightarrow\dfrac{a}{b}< \dfrac{a+n}{b+n}\left(n\in N^{\circledast}\right)\)

Ta có:

\(\dfrac{2005^{2016}+1}{2005^{2017}+1}< \dfrac{2005^{2016}+1+\left(2005^2-1\right)}{2005^{2017}+1+\left(2005^2-1\right)}=\dfrac{2005^{2016}+2005^2}{2005^{2017}+2005^2}=\dfrac{2005^2\left(2005^{2014}+1\right)}{2005^2\left(2005^{2015}+1\right)}=\dfrac{2005^{2014}+1}{2005^{2015}+1}\)

Vậy \(\dfrac{2005^{2016}+1}{2005^{2017}+1}< \dfrac{2005^{2014}+1}{2005^{2015}+1}\)

b,

\(\dfrac{19}{10}=\dfrac{10+9}{10}=\dfrac{10}{10}+\dfrac{9}{10}=1+\dfrac{9}{10}\\ \dfrac{49}{40}=\dfrac{40+9}{40}=\dfrac{40}{40}+\dfrac{9}{40}=1+\dfrac{9}{40}\)

Vì \(10< 40\Rightarrow\dfrac{9}{10}>\dfrac{9}{40}\Rightarrow1+\dfrac{9}{10}>1+\dfrac{9}{40}\Leftrightarrow\dfrac{19}{10}>\dfrac{49}{40}\)Vậy \(\dfrac{19}{10}>\dfrac{49}{40}\)

c,

\(\dfrac{13}{20}=\dfrac{20-7}{20}=\dfrac{20}{20}-\dfrac{7}{20}=1-\dfrac{7}{20}\\ \dfrac{33}{40}=\dfrac{40-7}{40}=\dfrac{40}{40}-\dfrac{7}{40}=1-\dfrac{7}{40}\)

Vì \(20< 40\Rightarrow\dfrac{7}{20}>\dfrac{7}{40}\Rightarrow1-\dfrac{7}{20}< 1-\dfrac{7}{40}\Leftrightarrow\dfrac{13}{20}< \dfrac{33}{40}\)

Vậy \(\dfrac{13}{20}< \dfrac{33}{40}\)

Áp dụng tính chất:

\(\dfrac{a}{b}< 1\Rightarrow\dfrac{a+m}{b+m}< 1\left(m\in N\right)\)

\(\)Đặt: \(B=\dfrac{2005^{2016}+1}{2005^{2017}+1}< 1\)

\(\Rightarrow B< \dfrac{2005^{2016}+1+4020024}{2005^{2017}+1+4020024}\)

\(B< \dfrac{2005^{2016}+4020025}{2005^{2017}+4020025}\)

\(B< \dfrac{2005^2\left(2005^{2014}+1\right)}{2005^2\left(2005^{2015}+1\right)}\)

\(B< \dfrac{2005^{2014}+1}{2005^{2015}+1}=A\)

\(B< A\)

\(\dfrac{48}{25}\cdot\dfrac{27}{55}+2\dfrac{4}{9}\cdot\dfrac{14}{33}\)

\(=\dfrac{1296}{1375}+\dfrac{22}{9}\cdot\dfrac{14}{33}\\ =\dfrac{1296}{1375}+\dfrac{28}{27}\\ =\dfrac{34992}{37125}+\dfrac{38500}{37125}\\ =\dfrac{73492}{37125}\)

\(1\dfrac{19}{22}\cdot\left(\dfrac{47}{77}-\dfrac{16}{15}\right)\\ =\dfrac{41}{22}\cdot\dfrac{-527}{1155}\\ =\dfrac{-21607}{25410}\)

\(\left(3\dfrac{10}{99}+4\dfrac{11}{99}-5\dfrac{8}{299}\right)-\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)\\ =\left(\dfrac{307}{99}+\dfrac{37}{99}-\dfrac{1503}{299}\right)-0\\ =\dfrac{344}{99}-\dfrac{1053}{299}\\ =-\dfrac{107}{2277}\)

a) Ta có: \(\dfrac{5}{8}+\dfrac{3}{17}+\dfrac{4}{18}+\dfrac{20}{-17}+\dfrac{-2}{9}+\dfrac{21}{56}\)

\(=\left(\dfrac{3}{17}-\dfrac{20}{17}\right)+\left(\dfrac{2}{9}-\dfrac{2}{9}\right)+\left(\dfrac{5}{8}+\dfrac{3}{8}\right)\)

\(=-1+1=0\)

b) Ta có: \(\left(\dfrac{9}{16}+\dfrac{8}{-27}\right)+\left(1+\dfrac{7}{16}+\dfrac{-19}{27}\right)\)

\(=\left(\dfrac{9}{16}+\dfrac{7}{16}\right)+\left(\dfrac{-8}{27}-\dfrac{19}{27}\right)+1\)

=1-1+1=1

help me!!!

a: Các phân số tối giản là 4/9; 17/13

b: Các phân số bằng 4/7 là 12/21; 36/63; 48/84;

a,\(\dfrac{4}{9},\dfrac{17}{13}\)

b,\(\dfrac{12}{21},\dfrac{36}{63},\dfrac{48}{84}\)

a)\(\dfrac{19}{48}-\dfrac{3}{40}=\dfrac{95}{240}-\dfrac{18}{240}=\dfrac{77}{240}\)

b)\(\dfrac{1}{6}+\dfrac{7}{27}+\dfrac{5}{18}=\dfrac{9}{54}+\dfrac{14}{54}+\dfrac{15}{54}=\dfrac{38}{54}=\dfrac{19}{27}\)

a) 19/48 - 3/40= 77/240

b) 1/6 + 7/27 + 5/18= 23/54 + 5/18= 19/27

a)\(\dfrac{19}{48}\) - \(\dfrac{3}{40}\)=\(\dfrac{77}{240}\)

b) \(\dfrac{1}{6}\)+\(\dfrac{7}{27}\)+\(\dfrac{5}{18}\)=\(\dfrac{23}{54}\)+\(\dfrac{5}{18}\)=\(\dfrac{19}{27}\)

\(a,\left(\dfrac{7}{20}+\dfrac{11}{15}-\dfrac{15}{12}\right):\left(\dfrac{11}{20}-\dfrac{26}{45}\right).\)

\(=\left(\dfrac{21}{60}+\dfrac{44}{60}-\dfrac{75}{60}\right):\left(\dfrac{99}{180}-\dfrac{104}{180}\right).\)

\(=\left(\dfrac{65}{60}-\dfrac{75}{60}\right):\left(-\dfrac{5}{180}\right).\)

\(=-\dfrac{10}{60}:\left(-\dfrac{5}{180}\right).\)

\(=-\dfrac{1}{6}:\left(-\dfrac{1}{36}\right).\)

\(=-\dfrac{1}{6}.\left(-36\right).\)

\(=\dfrac{-1.\left(-36\right)}{6}=\dfrac{36}{6}=6.\)

Vậy......

\(b,\dfrac{5-\dfrac{5}{3}+\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}+\dfrac{8}{9}-\dfrac{8}{27}}:\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{16}{121}}.\)

\(=\dfrac{5\left(1-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{27}\right)}{8\left(1-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{27}\right)}:\dfrac{15\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}{16\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}.\)

\(=\dfrac{5}{8}:\dfrac{15}{16}.\)

\(=\dfrac{5}{8}.\dfrac{16}{15}=\dfrac{5.16}{8.15}=\dfrac{1.2}{1.3}=\dfrac{2}{3}.\)

Vậy......

c, (làm tương tự câu b).

~ Học tốt!!! ~

\(a,=\dfrac{1}{10}+\dfrac{2}{10}+\dfrac{3}{10}+\dfrac{4}{10}+\dfrac{5}{10}+\dfrac{6}{10}+\dfrac{7}{10}+\dfrac{8}{10}+\dfrac{9}{10}=\dfrac{45}{10}=4,5\\ b,=\dfrac{4}{5}\times\left(\dfrac{3}{8}+\dfrac{5}{8}-\dfrac{7}{8}\right)\times2=\dfrac{8}{5}\times\dfrac{1}{8}=\dfrac{1}{5}=0,2\)

a) Rút gọn các phân số về tối giản, ta được:
\(\dfrac{1}{10}\)+\(\dfrac{2}{10}\)+\(\dfrac{3}{10}\)+\(\dfrac{4}{10}\)+\(\dfrac{5}{10}\)+\(\dfrac{6}{10}\)+\(\dfrac{7}{10}\)+\(\dfrac{8}{10}\)+\(\dfrac{9}{10}\)= kết quả là \(\dfrac{45}{10}\) ra số thập phân = \(4,5\)
b) \(\dfrac{4}{5}\) \(\times\) \(\left(\dfrac{3}{8}+\dfrac{5}{8}-\dfrac{7}{8}\right)\) = \(\dfrac{4}{5}\times\dfrac{1}{8}\) = \(\dfrac{4}{40}=\dfrac{1}{10}\)\(\div\dfrac{1}{2}\)
 = \(\dfrac{2}{10}=0,2\)