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Ta có: 1/1x2 + 1/2x3 + 1/3x4 +...+ 1/X x (X + 1) = 499/500
=> 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +...+ 1/X - 1/(X + 1) = 499/500
=> 1 - 1/(X + 1) = 499/500
=> 1/(X + 1) = 1 - 499/500
=> 1/(X + 1) = 1/500
=> X + 1 = 500
=> X = 500 - 1
=> X = 499
Đáp số: X = 499
\(\frac{3}{4}\times\frac{9}{7}\times\frac{11}{25}\)
\(=\frac{297}{700}\)
Chúc bn học tốt!!!!!
a) \(\frac{3}{5}\times y+\frac{1}{2}:\frac{5}{3}-\frac{5}{4}=\frac{1}{2}\times\frac{1}{3}\)
\(\Rightarrow\frac{3}{5}\times y+\frac{3}{10}-\frac{5}{4}=\frac{1}{6}\)
\(\Rightarrow\frac{3}{5}\times y+\left(-\frac{19}{20}\right)=\frac{1}{6}\)
\(\Rightarrow\frac{3}{5}\times y=\frac{67}{60}\)
\(\Rightarrow y=\frac{67}{36}\)
b) \(\frac{4}{5}:y+\frac{1}{4}\times\frac{1}{6}-\frac{1}{2}=\frac{1}{3}\times\frac{5}{2}\)
\(\Rightarrow\frac{4}{5}:y+\frac{1}{24}-\frac{1}{2}=\frac{5}{6}\)
\(\Rightarrow\frac{4}{5}:y+\left(-\frac{11}{24}\right)=\frac{5}{6}\)
\(\Rightarrow\frac{4}{5}:y=\frac{5}{6}+\frac{11}{24}=\frac{31}{24}\)
\(\Rightarrow y=\frac{4}{5}:\frac{31}{24}=\frac{96}{155}\)
c) \(\frac{3}{5}\times y-\frac{4}{5}:3+\frac{1}{12}=\frac{3}{2}+\frac{1}{5}\)
\(\Rightarrow\frac{3}{5}\times y-\frac{4}{15}+\frac{1}{12}=\frac{17}{10}\)
\(\Rightarrow\frac{3}{5}\times y-\frac{4}{15}=\frac{97}{60}\)
\(\Rightarrow\frac{3}{5}\times y=\frac{113}{60}\)
\(\Rightarrow y=\frac{113}{36}\)
\(\frac{1}{10}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{5}\cdot\frac{5}{4}\cdot\frac{4}{3}\cdot\frac{3}{2}=\frac{1}{10}\)
\(\frac{1}{10}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{5}\times\frac{5}{4}\times\frac{4}{3}\times\frac{3}{2}\)\(\frac{3}{2}\)
\(=\frac{1}{10}\times\left(\frac{2}{3}\times\frac{3}{2}\right)\times\left(\frac{3}{4}\times\frac{4}{3}\right)\times\left(\frac{4}{5}\times\frac{5}{4}\right)\times\left(\frac{5}{6}\times\frac{6}{5}\right)\)
\(=\frac{1}{10}\times1\times1\times1\times1\)
\(=\frac{1}{10}\)
#Chúc bạn học tốt !
#k cho mình nhé ?
\(x+\frac{1}{2}+x+\frac{1}{4}+x+\frac{1}{8}+x+\frac{1}{16}=\frac{23}{16}=>4x=\frac{23}{16}-\frac{15}{16}=\frac{1}{2}=>x=\frac{1}{8}\)
(xx4)+1/2+1/4+1/8+1/16=23/16
xx4=23/16-(1/2+1/4+1/8+1/16)
xx4=1/2
x=1/2:4
x=1/8
Đúng 100% nhé Nhớ k cho mình đấy
3636/4545+x=4848/1515
x=4848/1515-3636/4545
x=14544/4545-3636/4545
x=10908/4545
3535/5050-x=8/25
x=3535/5050-1616/5050
x=1919/5050
1/3x-2/5(x+1)=0
1/3x-2/5x-2/5=0
-1/15x-2/5=0
-1/15x=6/15
x=-6
\(A=\frac{1}{3}.x-\frac{2}{5}.\left(x+1\right)=\)\(0\)
\(A=\frac{1}{3}.x-\frac{2}{5}x-\frac{2}{5}\)\(=0\)
\(A=x.\left(\frac{1}{3}-\frac{2}{5}\right)-\frac{2}{5}\)\(=0\)
\(A=x.\frac{-1}{15}=\frac{2}{5}\)
\(A=\frac{2}{5}\div\frac{-1}{15}\)
\(A=-6\)
Vậy \(A=-6\)