Tính :
a, \(\dfrac{3\cdot13-13\cdot18}{15\cdot40-80}\);
b, \(\dfrac{18\cdot34+\left(-18\right)\cdot124}{-36\cdot17+9\cdot\left(-52\right)}\);
c, \(\dfrac{\dfrac{3}{41}-\dfrac{12}{47}+\dfrac{27}{53}}{\dfrac{4}{41}-\dfrac{16}{47}+\dfrac{36}{53}}+\dfrac{-0,25\cdot\dfrac{-2}{3}-0,75:\left(\dfrac{-1}{2}+\dfrac{2}{3}\right)}{\left|-1\dfrac{1}{2}\right|\cdot\left(\dfrac{-2}{3}-75\%:\dfrac{3}{-2}\right)}\).
Tìm x, biết:
a) \(\dfrac{3}{4.7}+\dfrac{3}{7.10}+....+\dfrac{3}{x\left(x+3\right)}=\dfrac{9}{38}\)
b) \(\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{9}\)
Tính
\(B=\dfrac{1}{4}+\dfrac{1}{12}+\dfrac{1}{36}+\dfrac{1}{108}+\dfrac{1}{324}+\dfrac{1}{972}\)
tinh nhanh
\(\dfrac{25}{100}+\dfrac{14}{21}-\dfrac{31}{62}-\dfrac{-15}{40}+\dfrac{-27}{45}-\dfrac{-36}{135}\)
Bài 2: Tính
D =\(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+....+\dfrac{1}{29}\)
E = \(\dfrac{1}{4}+\dfrac{1}{12}+\dfrac{1}{36}+\dfrac{1}{108}+\dfrac{1}{972}\)
\(\left(\dfrac{1}{3}-\dfrac{1}{2}\right)^{x-2}=\dfrac{1}{216}\)
\(\left[\left(\dfrac{1}{3}-\dfrac{1}{2}\right)^{x-5}\right]^{x-1}=\dfrac{1}{36}\)
Tìm \(x\in N\), biết :
a)\(\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{2}{29}\)
Tìm x biết \(\dfrac{x}{6}+\dfrac{x}{10}+\dfrac{x}{15}+\dfrac{x}{21}+\dfrac{x}{28}+\dfrac{x}{36}+\dfrac{x}{45}+\dfrac{x}{55}+\dfrac{x}{66}+\dfrac{x}{78}=\dfrac{220}{39}\)
so sánh
a. \(\dfrac{31}{58}va\dfrac{57}{59}\)
b. \(\dfrac{-58}{53}va\dfrac{-36}{55}\)