\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{996}{997}\)
\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}\)= \(\dfrac{996}{997}\) \(1-\dfrac{1}{x+1}\) = \(\dfrac{996}{997}\)
\(\dfrac{1}{x+1}\) = \(1-\dfrac{996}{997}\)
\(\dfrac{1}{x+1}\) =\(\dfrac{1}{997}\)
\(\Rightarrow\) x + 1 = 997
x = 997 - 1
x = 996
Vậy x = 996
Tìm số nguyên x biết:
a) \(-4\dfrac{3}{5}\) x \(2\dfrac{4}{3}\) \(\le\) x \(\le\) \(-2\dfrac{3}{5}\) : \(1\dfrac{6}{15}\)
b) \(-4\dfrac{1}{3}\) (\(\dfrac{1}{2}-\dfrac{1}{6}\) ) \(\le\) x \(\le\dfrac{2}{3}\left(\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{3}{7}\right)\)
c) \(\dfrac{x+1}{35}+\dfrac{x+2}{34}+\dfrac{x+3}{33}=\dfrac{x+4}{32}+\dfrac{x+5}{31}\dfrac{x+6}{30}\)
\(\dfrac{1}{7}-\dfrac{8}{7}:8-3:\dfrac{3}{4}\cdot\left(-2\right)^2\)
\(\dfrac{1}{2}\)-x + \(\dfrac{2}{3}\)x -1 = -3\(\dfrac{1}{3}\)
\(\dfrac{-5}{6}\) + \(\dfrac{8}{3}\) + \(\dfrac{-29}{6}\) ≤ x ≤ \(\dfrac{-1}{2}\) + 2 + \(\dfrac{5}{2}\)
( 2,7x - 1\(\dfrac{1}{2}\)x) : \(\dfrac{2}{7}\)= \(\dfrac{-21}{4}\)
tính giá trị biểu thức sau một cách hợp lí :
\(A=\dfrac{-10}{3}+\dfrac{19}{6}.\dfrac{7}{5}-\dfrac{19}{3}.\dfrac{1}{10}+\dfrac{19}{10}.\dfrac{4}{3}\)
\(M=\dfrac{1+2+2^2+2^3+....+2^{2012}}{2^{2014}-2}\)
1) Tính
B=(1+\(\dfrac{1}{2}\)).(1+\(\dfrac{1}{3}\)).(\(1+\dfrac{1}{4}\)).....(\(1+\dfrac{1}{99}\))
tìm x:
\(\dfrac{x+1}{3}\)= \(\dfrac{-3}{-9}\)
Tìm x thuộc Z,biết:
\(\dfrac{-2}{7}\)<\(\dfrac{x}{3}\)<\(\dfrac{11}{4}\)
