Ôn tập chương III

\(C=\dfrac{15^{2016}-3+5}{15^{2016}-3}=1+\dfrac{5}{15^{2016}-3}\)

\(D=\dfrac{15^{2016}-2+5}{15^{2016}-2}=1+\dfrac{5}{15^{2016}-2}\)

mà \(15^{2016}-3< 15^{2016}-2\)

nên C>D

\(=\left(\dfrac{3}{2}-\dfrac{5}{6}+\dfrac{7}{12}\right)+\left(-\dfrac{9}{20}+\dfrac{11}{30}\right)+\left(\dfrac{-13}{42}+\dfrac{15}{56}\right)\)

\(=\dfrac{18-10+7}{12}+\dfrac{-27+22}{60}+\dfrac{-1}{24}\)

\(=\dfrac{15}{12}+\dfrac{-5}{60}+\dfrac{-1}{24}\)

\(=\dfrac{30-1+\left(-2\right)}{24}=\dfrac{27}{24}=\dfrac{9}{8}\)

a) A= \(\dfrac{12}{19}.\dfrac{7}{15}.\dfrac{-13}{17}.\dfrac{19}{12}.\dfrac{17}{13}\)

A = 1 . ( - 1 ) . \(\dfrac{7}{15}\)

A = ( - 1 ) . \(\dfrac{7}{15}\)

A = \(\dfrac{-7}{15}\)

b) B = \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+......+\dfrac{1}{9.10}\)

B = \(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+.....+\dfrac{1}{9}-\dfrac{1}{10}\)

B = 1 - \(\dfrac{1}{10}\)

B = \(\dfrac{9}{10}\)

c) C = \(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{97.99}\)

C = \(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}\)

C = \(\dfrac{1}{3}-\dfrac{1}{99}\)

C =\(\dfrac{32}{99}\)

Câu d) làm tương tự như câu c)

Bài 5

Phân số chỉ số sách đọc trong ngày 3 là:

\(1-\left(\dfrac{1}{3}+\dfrac{5}{8}\right)\)=\(\dfrac{1}{24}\)( quyển sách )

⇒ \(\dfrac{1}{24}\)quyển sách là 90 trang

Số trang của cuốn sách đó là:

\(90:\dfrac{1}{24}\) = 2160 ( trang)

Câu 4 làm tương tự nha

=>x(1-7/12+3/7)=5/4

=>71/84x=5/4

hay x=105/71

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+.......+\dfrac{1}{x\left(x+1\right)}=\dfrac{44}{45}\)

=> \(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}+......+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{44}{45}\)

=> \(1-\dfrac{1}{x+1}=\dfrac{44}{45}\)

=> \(\dfrac{x+1}{x+1}-\dfrac{1}{x+1}=\dfrac{44}{45}\)

=> \(\dfrac{x+1-1}{x+1}=\dfrac{44}{45}\)

=> \(\dfrac{x}{x+1}=\dfrac{44}{45}\)

=> 44(x+1)=45x

=> 44x+44=45x

=> 44x-45x=-44

=> -1x=-44

=> x=44

vậy x=44

a: \(=\dfrac{5}{\dfrac{2}{5}}\cdot\dfrac{4}{\dfrac{2}{7}}+\dfrac{5}{\dfrac{5}{7}}\cdot\dfrac{5}{\dfrac{2}{5}}\)

\(=5\cdot\dfrac{5}{2}\cdot4\cdot\dfrac{7}{2}+5\cdot\dfrac{5}{2}\cdot5\cdot\dfrac{7}{5}\)

\(=\dfrac{25}{2}\left(14+7\right)=\dfrac{25}{2}\cdot21=\dfrac{525}{2}\)

b: \(=\dfrac{3}{4}-2+\dfrac{1}{2}\cdot\dfrac{12}{5}-\dfrac{1}{4}\)

\(=\dfrac{6}{5}-2+\dfrac{1}{2}=-\dfrac{3}{10}\)

gọi \(A=\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{30}}\)

\(\Leftrightarrow2A=1+\dfrac{1}{2}+...+\dfrac{1}{2^{29}}\)

\(\Leftrightarrow2A-A=(1+\dfrac{1}{2}+...+\dfrac{1}{2^{29}})-\left(\dfrac{1}{2}+...+\dfrac{1}{2^{30}}\right)\)

\(\Leftrightarrow A=1-\dfrac{1}{2^{30}}< 1\)

đpcm