Cho M = 1/2 . 3/4 . 5/6. ... . 799/800
So sánh M với 1/28 và 1/40.
Ai làm đúng tớ sẽ cho 1 tick!
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5/4-yx5/6=-1/12
5/4-y = -1/12:5/6
5/4-y = -1/10
y = 5/4-(-1/10)
y = 27/20
\(\frac{5}{4}-y.\frac{5}{6}=\frac{1}{4}-\frac{1}{3}\)
\(\Rightarrow\frac{5}{4}-y.\frac{5}{6}=-\frac{1}{12}\)
\(\Rightarrow y.\frac{5}{6}=\frac{5}{4}-\left(-\frac{1}{12}\right)\)
\(\Rightarrow y.\frac{5}{6}=\frac{5}{4}+\frac{1}{12}\)
\(\Rightarrow y.\frac{5}{6}=\frac{4}{3}\)
\(\Rightarrow y=\frac{4}{3}:\frac{5}{6}\)
\(\Rightarrow y=\frac{8}{5}\)
Vậy \(y=\frac{8}{5}.\)
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2019.2020}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{2019}-\frac{1}{2020}\)
\(=1-\frac{1}{2020}>1\)
M = \(\frac{1}{5}+\left(\frac{1}{5}\right)^2+\left(\frac{1}{5}\right)^3+...+\left(\frac{1}{5}\right)^{^{^{ }}50}\)
=> 5M = 1 + \(\frac{1}{5}+\left(\frac{1}{5}\right)^2+...+\left(\frac{1}{5}\right)^{49}\)
=> 5M - M = ( 1 + \(\frac{1}{5}+\left(\frac{1}{5}\right)^2+...+\left(\frac{1}{5}\right)^{49}\)) - ( \(\frac{1}{5}+\left(\frac{1}{5}\right)^2+\left(\frac{1}{5}\right)^3+...+\left(\frac{1}{5}\right)^{^{^{ }}50}\))
4M = 1 - \(\left(\frac{1}{5}\right)^{50}\)
=> M = \(\frac{1-\left(\frac{1}{5}\right)^{50}}{4}\)< \(\frac{1}{4}\)
a) Vì 4 < 5 nên \(\frac{3}{4}>\frac{3}{5}\)
b) Vì 4 < 5 nên \(\frac{4}{7}< \frac{5}{7}\)
c) Ta có :
\(\frac{2}{7}=\frac{2\times5}{7\times5}=\frac{10}{35}\)
\(\frac{4}{5}=\frac{4\times7}{5\times7}=\frac{28}{35}\)
Vì 10 < 28 nên \(\frac{10}{35}< \frac{28}{35}\)hay \(\frac{2}{7}< \frac{4}{5}\)
d) Ta có :
\(\frac{8}{9}=\frac{8\times10}{9\times10}=\frac{80}{90}\)
\(\frac{9}{10}=\frac{9\times9}{10\times9}=\frac{81}{90}\)
Vì 80 < 81 nên \(\frac{80}{90}< \frac{81}{90}\)hay \(\frac{8}{9}< \frac{9}{10}\)
e) Ta có :
\(\frac{10}{9}=\frac{10\times2}{9\times2}=\frac{20}{18}\)
Vì 19 < 20 nên \(\frac{19}{18}< \frac{20}{18}\)hay \(\frac{19}{18}< \frac{10}{9}\)
f) Ta có :
\(\frac{8}{3}=\frac{8\times4}{3\times4}=\frac{32}{12}\)
\(\frac{5}{6}=\frac{5\times2}{6\times2}=\frac{10}{12}\)
Vì 32 > 10 nên \(\frac{32}{12}>\frac{10}{12}\)hay \(\frac{8}{3}>\frac{5}{6}\)
a) 2n^3 + 2n^2 - 2n^3 - 2n^2 + 6n = 6n chia hết 6
b) 3n - 2n^2 - ( n + 4n^2 - 1 - 4n ) - 1
= 3n - 2n^2 - n - 4n^2 + 1 + 4n -1
= 6n - 6n^2 chia hết 6
c) m^3 + 8 - m^3 + m^2 - 9 - m^2 - 18
= - 19
Bài 1:
\(2n^2\left(n+1\right)-2n\left(n^2+n-3\right)\)
\(=2n\left(n^2+n-n^2-n+3\right)\)
\(=6n\)\(⋮\)\(6\)
Bài 2:
\(n\left(3-2n\right)-\left(n-1\right)\left(1+4n\right)-1\)
\(=3n-2n^2-\left(n+4n^2-1-4n\right)-1\)
\(=6n-6n^2=6\left(n-n^2\right)\)\(⋮\)\(6\)
Bài 3:
\(\left(m^2-2m+4\right)\left(m+2\right)-m^3+\left(m+3\right)\left(m-3\right)-m^2-18\)
\(=m^3+8-m^3+m^2-9-m^2-18\)
\(=-19\)
\(\Rightarrow\)đpcm
\(\dfrac{3}{5}\times\dfrac{4}{7}\times1\dfrac{1}{2}\)
\(=\dfrac{3}{5}\times\dfrac{4}{7}\times\dfrac{3}{2}\)
\(=\dfrac{3\times4\times3}{5\times7\times2}\)
\(=\dfrac{3\times2\times3}{5\times7}\)
\(=\dfrac{18}{35}\)