Chứng minh rằng:
a) \(\dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+...\dfrac{2018}{2019!}\)<1
b) \(\dfrac{1.2-1}{2!}+\dfrac{2.3-1}{3!}+...+\dfrac{999.1000-1}{1000!}\)<2
Chứng minh rằng :
\(\dfrac{1}{1\cdot2}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{49\cdot50}=\dfrac{1}{26}+\dfrac{1}{27}+...+\dfrac{1}{50}\)
Chứng minh rằng: \(\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+...+\dfrac{1}{97.100}< \dfrac{1}{3}\)
a) Chứng tỏ rằng nếu \(\dfrac{a}{c}< \dfrac{c}{d}\left(b>0,d>0\right)\) thì \(\dfrac{a}{b}< \dfrac{a+c}{b+d}< \dfrac{c}{d}\)
b) Hãy viết ba số hữu tỉ xen giữa \(-\dfrac{1}{3}\) và \(-\dfrac{1}{4}\)
Thực hiện phép tính :
a ) \(1-\dfrac{1}{2}:\dfrac{-3}{2}+\dfrac{2}{3}\)
b ) \(\dfrac{-3}{4}-\dfrac{-7}{2}+\dfrac{2}{-3}\)
c ) \(0,25-3\dfrac{1}{2}:\dfrac{1}{2}+\dfrac{-3}{4}.\dfrac{2}{-3}\)
Thực hiện phép tính:
a) \(\left(\dfrac{9}{25}-2.18\right):\left(3\dfrac{4}{5}+0,2\right)\)
b) \(\dfrac{3}{8}.19\dfrac{1}{3}-\dfrac{3}{8}.33\dfrac{1}{3}\)
c) \(1\dfrac{4}{23}+\dfrac{5}{21}-\dfrac{4}{23}+0,5+\dfrac{16}{21}\)
d) \(\dfrac{21}{47}+\dfrac{9}{45}+\dfrac{26}{47}+\dfrac{4}{5}\)
e) \(\dfrac{15}{12}+\dfrac{5}{13}-\dfrac{3}{12}-\dfrac{18}{13}\)
a, Tìm tất cả các số tự nhiên n sao cho số A=\(\dfrac{1-6n}{2n-3}\) là một số nguyên.
b,Cho các phân số \(\dfrac{ab}{a+2b}\)=\(\dfrac{3}{2}\); \(\dfrac{bc}{b+2c}\)=\(\dfrac{4}{3}\);\(\dfrac{ca}{c+2a}\)=3 . Rút gọn phân số : T=\(\dfrac{abc}{ab+bc+ca}\)
Tìm x, biết:
a) \(\dfrac{-3}{7}+x=\dfrac{1}{3}\)
b) \(\dfrac{3}{4}+\dfrac{1}{4}:x=\dfrac{2}{5}\)
c) \(1\dfrac{1}{3}:0,8=\dfrac{2}{3}:0,1x\)
d) \(\left|x-3\right|=\dfrac{1}{2}\)
11) \(\dfrac{1}{3}\)x + \(\dfrac{1}{5}\) - \(\dfrac{1}{2}\)x = 1\(\dfrac{1}{4}\)
12) \(\dfrac{3}{2}\)( x + \(\dfrac{1}{2}\)) - \(\dfrac{1}{8}\)x = \(\dfrac{1}{4}\)
13) \(\dfrac{3}{5}\)( x + \(\dfrac{1}{3}\)) - \(\dfrac{1}{3}\)( x - \(\dfrac{1}{2}\)) = 1\(\dfrac{1}{3}\)
14) \(\dfrac{2}{5}\)( x + \(\dfrac{1}{2}\)) = \(\dfrac{3}{4}\)( x - \(\dfrac{1}{5}\))
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