Ta có: \(\left(\dfrac{1}{2}\right)^2.\left(\dfrac{2}{3}\right)^2...\left(\dfrac{9}{10}\right)^2=\dfrac{1^2}{2^2}.\dfrac{2^2}{3^2}...\dfrac{9^2}{10^2}=\dfrac{1^2.2^2...9^2}{2^2.3^2...10^2}=\dfrac{1^2}{10^2}\)
Bài 1: Tính
a) \(\dfrac{1}{5}:\dfrac{1}{10}-\dfrac{1}{3}\left(\dfrac{6}{5}-\dfrac{9}{4}\right)\)
b) \(\dfrac{1}{2}\left(\dfrac{4}{3}+\dfrac{2}{5}\right)-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)\)
c) \(\dfrac{6}{7}:\left(\dfrac{3}{26}-\dfrac{3}{13}\right)+\dfrac{6}{7}\left(\dfrac{1}{10}-\dfrac{8}{5}\right)\)
Tính giá trị biểu thức bằng cách hợp lý nhất:
P=\(\dfrac{2}{3}-\left(-\dfrac{1}{4}\right)+\dfrac{3}{5}-\dfrac{7}{45}-\left(-\dfrac{5}{9}\right)+\dfrac{1}{2}+\dfrac{1}{35}\)
ĐỀ 1:
1. Tính:
a. \(\dfrac{7}{23}\left[\left(\dfrac{-8}{6}\right)-\dfrac{45}{18}\right]\)
b. \(\dfrac{1}{5}:\dfrac{1}{10}-\dfrac{1}{3}\left(\dfrac{6}{5}-\dfrac{9}{4}\right)\)
c. \(\dfrac{3}{5}.\left(\dfrac{-8}{3}\right)-\dfrac{3}{5}:\left(-6\right)\)
d. \(\dfrac{1}{2}\left(\dfrac{4}{3}+\dfrac{2}{5}\right)-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)\)
e. \(\dfrac{6}{7}:\left(\dfrac{3}{26}-\dfrac{3}{13}\right)+\dfrac{6}{7}\left(\dfrac{1}{10}-\dfrac{8}{5}\right)\)
2. Tìm x, biết:
a. \(1\dfrac{2}{5}x+\dfrac{3}{7}=\dfrac{4}{5}\)
b. |x - 1,5| = 2
c. \(\dfrac{4}{5}-\left|x-\dfrac{1}{6}\right|=\dfrac{2}{3}\)
d. 3x . 2x = 216
e. \(\dfrac{1}{2}\left(x-\dfrac{1}{3}\right)+\dfrac{-1}{2}=\dfrac{3}{4}\)
* Lm nhanh nha
Ths you <3
Cho C = \(\left(\dfrac{1}{2^2}-1\right)\left(\dfrac{1}{3^2}-1\right)...\left(\dfrac{1}{10^2}-1\right)xy^2z^3t^4\)
D= \(\left(1+\dfrac{7}{9}\right)\left(1+\dfrac{7}{20}\right)\left(1+\dfrac{7}{33}\right)...\left(1+\dfrac{7}{180}\right)x^4y^3z^2t\)
Tính E biết E = \(\dfrac{90}{11^2}CD\)
a,\(\dfrac{2}{3}+5\dfrac{3}{7}:2+\dfrac{9}{49}.\left(-7\right)+\dfrac{1}{12}.\left(-2\right)^4\)
b,\(2\dfrac{3}{4}.\left(-0,4\right)-1\dfrac{3}{5}.2,75+\left(-1,2\right):\dfrac{4}{11}\)
Tính giá trị biểu thức bằng cách hợp lý:
A=(\(\left(5-\dfrac{3}{4}+\dfrac{1}{5}\right)-\left(6+\dfrac{7}{4}-\dfrac{8}{5}\right)-\left(2-\dfrac{5}{4}+\dfrac{16}{5}\right)\)
Tính
B=\(\dfrac{\left(\dfrac{2}{3}\right)^3.\left(\dfrac{-3}{4}\right)^2.\left(-1\right)^{2011}}{\left(\dfrac{2}{5}\right)^2.\left(\dfrac{-5}{12}\right)^3}\)
Tính giá trị của biểu thức sau:
A = \(\dfrac{1}{2}\left(1+\dfrac{1}{1.3}\right)\left(1+\dfrac{1}{2.4}\right)\left(1+\dfrac{1}{3.5}\right)...\left(1+\dfrac{1}{2015.2017}\right)\)
Tính giá trị của biểu thức sau:
A= \(\dfrac{1}{2}\left(1+\dfrac{1}{1.3}\right)\left(1+\dfrac{1}{2.4}\right)\left(1+\dfrac{1}{3.5}\right)...\left(1+\dfrac{1}{2015.2017}\right)\)