\(l=\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+....+\dfrac{1}{97.100}\)
\(=\dfrac{1}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\)
\(=\dfrac{1}{3}\left(1-\dfrac{1}{100}\right)=\dfrac{1}{3}-\dfrac{1}{300}< \dfrac{1}{3}\left(đpcm\right)\)
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:
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 :A=\(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{16}\)không phải là 1 số nguyên
\(\dfrac{0,75+\dfrac{3}{5}-\dfrac{3}{7}-\dfrac{3}{13}}{2,75+2\dfrac{1}{5}-\dfrac{11}{7}-\dfrac{11}{3}}-\dfrac{0,75-\dfrac{3}{11}-\dfrac{1}{3}}{\dfrac{5}{22}-0,625+\dfrac{5}{18}}\)
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 \(-\dfrac{1}{4}\)
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 - \(\dfrac{1}{5}\))
Giup mik nha mik cần gấp
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 ) \(0,25-3\dfrac{1}{2}:\dfrac{1}{2}+\dfrac{-3}{4}.\dfrac{2}{-3}\)
Tìm x biết:
a) \(\dfrac{x+1}{10}+\dfrac{x+1}{11}+\dfrac{x+1}{12}=\dfrac{x+1}{13}+\dfrac{x+1}{14}\)
b)\(\dfrac{x+4}{2010}+\dfrac{x+3}{2010}=\dfrac{x+2}{2012}+\dfrac{x+1}{2013}\)
a) -12=\(\dfrac{-12}{1}\)
b) 2,1=\(\dfrac{21}{10}\)
c) -7\(\dfrac{1}{3}\)=\(\dfrac{-22}{3}\)
d) 19%=\(\dfrac{19}{100}\)
