a, Chứng tỏ rằng: \(\dfrac{12n+1}{30n+2}\) là phân số tối giản.
b, Chứng minh rằng: \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{100^2}< 1\)
Cho A=\(\dfrac{1}{2^2}\)+\(\dfrac{1}{3^2}\)+\(\dfrac{1}{4^2}\)+........+\(\dfrac{1}{100^2}\).Chứng minh rằng A<\(\dfrac{3}{4}\)
Cho A= \(\dfrac{1}{4^2}+\dfrac{1}{6^2}+\dfrac{1}{8^2}+\dfrac{1}{10^2}+...+\dfrac{1}{160^2}\)
Chứng minh: \(\dfrac{1}{8}< A< \dfrac{3}{16}\)
CMR: \(\dfrac{200-\left(3+\dfrac{2}{3}+\dfrac{2}{4}+\dfrac{2}{5}+...+\dfrac{2}{100}\right)}{\dfrac{1}{2}+\dfrac{2}{3}+\dfrac{3}{4}+...+\dfrac{99}{100}}=2\)
Helppp!!!
tính
a) (\(2\dfrac{5}{6}+1\dfrac{4}{9}\)):(\(10\dfrac{1}{12}\)-9\(\dfrac{1}{2}\))
b) \(\dfrac{0,8:\left(\dfrac{4}{5}:1,25\right)}{0,64-\dfrac{1}{25}}\)
c) \(\dfrac{\left(100-\dfrac{2}{25}\right):\dfrac{4}{7}}{\left(6\dfrac{5}{9}-3\dfrac{1}{4}\right).2\dfrac{2}{27}}\) + (1,2 . 0,5) : \(\dfrac{3}{5}\)
Tìm y:
-y:\(\dfrac{1}{2}\)-\(\dfrac{5}{2}\)=4\(\dfrac{1}{2}\)
Tính:
N = \(\dfrac{3}{4}\).\(\dfrac{8}{9}\).\(\dfrac{15}{16}\)....\(\dfrac{899}{900}\).\(\dfrac{960}{961}\)
S=\(\dfrac{1}{1.2.3}\)+\(\dfrac{1}{2.3.4}\)+\(\dfrac{1}{3.4.5}\)+...+\(\dfrac{1}{10.11.12}\)+\(\dfrac{1}{11.12.13}\)
Tìm x, biết:
a, \(\left(2\dfrac{3}{4}-1\dfrac{4}{5}\right)x=1\)
b, \(x^2-9\) \(3-5x=0\)
c, \(\left|3x-1\right|+2\dfrac{3}{4}=3\dfrac{1}{16}\)
Tính :
a) \(\dfrac{1}{3}+\dfrac{3}{8}-\dfrac{7}{12}\)
b) \(\dfrac{-3}{14}+\dfrac{5}{8}-\dfrac{1}{2}\)
c) \(\dfrac{1}{4}-\dfrac{2}{3}-\dfrac{11}{18}\)
d) \(\dfrac{1}{4}+\dfrac{5}{12}-\dfrac{1}{13}-\dfrac{7}{8}\)
\(\dfrac{2}{7}.\dfrac{4}{5}+\dfrac{3}{5}.\dfrac{2}{7}-\dfrac{1}{5}\)