\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{19}\right)\left(1-\frac{1}{20}\right)\)

\(A=\left(\frac{2}{2}-\frac{1}{2}\right)\left(\frac{3}{3}-\frac{1}{3}\right)...\left(\frac{19}{19}-\frac{1}{19}\right)\left(\frac{20}{20}-\frac{1}{20}\right)\)

\(A=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{18}{19}.\frac{19}{20}\)

\(A=\frac{1.2.3...18.19}{2.3.4...19.20}\)

\(A=\frac{1}{20}\Leftrightarrow A>\frac{1}{21}\)

\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right).....\left(1-\frac{1}{20}\right)\)

\(A=\frac{1}{2}.\frac{2}{3}......\frac{19}{20}=\frac{1}{20}>\frac{1}{21}\)

\(\text{Vậy: A lớn hơn 1/21}\)

mik ko biết !

THIÊn Lý

x+y=1

<=> x=1-y

<=>P=(1-y)y=\(y-y^2\)

<=>P=\(\frac{1}{4}-\left(y^2-y+\frac{1}{4}\right)\)

<=>P=\(\frac{1}{4}-\left(y-\frac{1}{2}\right)^2\le\frac{1}{4}\)

=>Max của P=\(\frac{1}{4}\)<=>y=\(\frac{1}{2}\)

x+y=1

\(\Rightarrow x=1-y\)

\(\Rightarrow P=x.y=\left(1-y\right).y=y-y^2=-\left(y^2-y\right)\)

\(\Rightarrow P=-\left(y^2-2.y.\frac{1}{2}+\left(\frac{1}{2}\right)^2-\left(\frac{1}{2}\right)^2\right)\)

\(\Rightarrow P=-\left(y^2-2.y.\frac{1}{2}+\frac{1}{4}\right)+\frac{1}{4}\)

\(\Rightarrow P=-\left(y-\frac{1}{2}\right)^2+\frac{1}{4}\)

Vì :\(\left(y-\frac{1}{2}\right)^2\ge0\)

\(\Rightarrow-\left(y-\frac{1}{2}\right)^2\le0\)

\(\Rightarrow P\le\frac{1}{4}\)

\(\Rightarrow GTLN\)của\(P=\frac{1}{4}\)khi : \(y=\frac{1}{2}\)

\(\Rightarrow x=1-\frac{1}{2}=\frac{1}{2}\)

\(Q=\frac{2^{12}.3^5-4^6.81}{\left(2^2.3\right)^6+8^4.3^5}=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}\)

\(=\frac{2^{12}.3^4.\left(3-1\right)}{2^{12}.3^5.\left(3+1\right)}=\frac{2}{3.4}=\frac{1}{6}\)

Q = \(\frac{2^{12}.3^5-4^6.81}{\left(2^2.3\right)^6+8^4.3^5}\)

    = \(\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}\)

    = \(\frac{2^{12}.3^4.\left(3-1\right)}{2^{12}.3^5.\left(3+1\right)}\)

    = \(\frac{2}{3.4}=\frac{1}{6}\)

\(P=\frac{n+2}{n-7}=\frac{n-7+9}{n-7}=1+\frac{9}{n-7}\)

P max => \(\frac{9}{n-7}max\)=> n-7 min và n-7>0 vì 9>0 và không đổi

=> n-7=1 => n=8

Vậy....