A = 2/1*5 + 2/5*9 + ... + 2/101*105

   = 1/2(4/1*5 + 4/5*9 + ... + 4/101*105)

   = 1/2(1 - 1/5 + 1/5 - 1/9 + ... + 1/101 - 1/105)

   = 1/2(1 - 1/105)

   = 1/2 * 104/105 = 52/105

Sửa câu b. Phân số thứ 2 phải là 4/5*8

B = 4/2*5 + 4/5*8 + ... + 4/47*50

   = 4/3(3/2*5 + 3/5*8 + ... + 3/47*50)

   = 4/3(1/2 - 1/5 + 1/5 - 1/8 + ... + 1/47 - 1/50)

   = 4/3(1/2 - 1/50)

   = 4/3 * 24/50 = 16/25

A= 24640

các bạn cho minhf cách làm nhé!

Tính nhanh:

a) 1-2-3+4+5-6-7+8+9-10-.......+200+201-202-203

Đặt \(A=\text{1-2-3+4+5-6-7+8+9-10-.......+200+201-202-203}\)

\(A=1+\left(2-3-4+5\right)+\left(6-7-8=9\right)+\left(10-11-12+13\right)+... \)\(+\left(298-299-300+301\right)+302\)

\(A=1+0+0+0+...+0+302\)

\(A=1+302\)

\(A=303\)

Phần B làm sau nha!

Ta có 1/2*3=1/2-1/3;

         1/3*4=1/3-1/4

       ......................(tương tự với các số khác)

         1/149*150=1/149-1/150

=>A=1/2-1/3+1/3-1/4+1/4-1/5+...-1/149+1/149-1/150=1/2-1/150

A=75/150-1/150=74/150=37/75

Vậy A= 37/75

  \(\dfrac{1}{2}+\dfrac{3}{4}-\left(\dfrac{3}{4}-\dfrac{4}{5}\right)\)

=\(\dfrac{1}{2}+\dfrac{3}{4}-\dfrac{3}{4}+\dfrac{4}{5}\)

=\(\left(\dfrac{1}{2}+\dfrac{4}{5}\right)+\left(\dfrac{3}{4}-\dfrac{3}{4}\right)\) 

=\(\left(\dfrac{5}{10}+\dfrac{8}{10}\right)+0\)

=\(\dfrac{13}{10}\)

\(-\dfrac{7}{25}.\dfrac{11}{13}+\left(-\dfrac{7}{25}\right).\dfrac{2}{13}-\dfrac{18}{25}\)

=\(-\dfrac{7}{25}.\cdot\left(\dfrac{11}{13}+\dfrac{2}{13}\right)-\dfrac{18}{25}\) 

=\(-\dfrac{7}{25}.1-\dfrac{18}{25}\) 

=\(-\dfrac{7}{25}-\dfrac{18}{25}\) 

=\(-\dfrac{25}{25}\) = \(-1\)

A=1/2-1/3+1/3-1/4+...+1/149-1/150

=1/2-1/150

=37/75

B=3A=37/25

a)\(-\dfrac{2}{5}.\dfrac{4}{7}+\dfrac{-3}{5}.\dfrac{2}{7}+\dfrac{-3}{5}\) 

=\(-\dfrac{2}{5}.\dfrac{4}{7}+\dfrac{3}{7}.\dfrac{-2}{5}+\dfrac{-3}{5}\)

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

=\(\dfrac{-2}{5}.1+\dfrac{-3}{5}\) 

=\(-\dfrac{2}{5}+\dfrac{-3}{5}\) 

=\(-\dfrac{5}{5}\) = -1

\(\dfrac{5}{9}.\dfrac{14}{17}+\dfrac{1}{17}.\dfrac{5}{9}+\dfrac{2}{9}+\dfrac{5}{12}\)

=\(\dfrac{5}{9}.\left(\dfrac{14}{17}+\dfrac{1}{17}\right)+\dfrac{2}{9}+\dfrac{5}{12}\) 

=\(\dfrac{5}{9}.\dfrac{15}{17}+\dfrac{2}{9}+\dfrac{5}{12}\) 

=\(\dfrac{25}{51}+\dfrac{2}{9}+\dfrac{5}{12}\)

=\(\dfrac{691}{612}\)