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\(A=3\left(\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+.....+\frac{3}{55\cdot58}\right)\)
\(A=3\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+.....+\frac{1}{55}-\frac{1}{58}\right)\)
\(A=3\left(1-\frac{1}{58}\right)\)
\(A=3-\frac{1}{174}< 3< \frac{10}{3}\)
S= - 32\(\left(\frac{1}{4}+\frac{1}{28}+\frac{1}{70}+...+\frac{1}{868}\right)\)
S = - 32\(\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{28.31}\right)\)
S = - 3\(\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{28.31}\right)\)
S = -3\(\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{28}-\frac{1}{31}\right)\)
S = -3 \(\left(1-\frac{1}{31}\right)\)
S = -3\(.\frac{30}{31}\)
S = -90/31
1/3S=-(1/1*4+1/4*7+1/7*10+...+1/28*31)=-(1/1-1/4+1/4-1/7+1/7-1/10+...+1/28-1/31)=-(1/1-1/31)=-30/31
=>S=(-30/31):1/3=-90/31
Làm không biết đúng không nha :D
\(2^{3^{2^3}}=\left(\left(2^3\right)^2\right)^3=\left(8^2\right)^3=8^6\)
\(3^{2^{3^2}}=\left(\left(3^2\right)^3\right)^2=\left(9^3\right)^2=9^6\)
\(\Rightarrow\)
Ta có :
\(A=\frac{2016^{2016}+2}{2016^{2016}-1}=\frac{\left(2016^{2016}-1\right)+3}{2016^{2016}-1}=1+\frac{3}{2016^{2016}-1}\)
\(B=\frac{2016^{2016}}{2016^{2016}-3}=\frac{\left(2016^{2016}-3\right)+3}{2016^{2016}-3}=1+\frac{3}{2016^{2016}-3}\)
Vì \(2016^{2016}-1>2016^{2016}-3\) nên \(\frac{3}{2016^{2016}-1}< \frac{3}{2016^{2016}-3}\)
\(\Rightarrow1+\frac{3}{2016^{2016}-1}< 1+\frac{3}{2016^{2016}-3}\)
\(\Rightarrow A< B\)
2^3^2^3= (2^3)^(2^3)=8^8
3^2^3^2=(3^2)^(3^2)=9^9
8^8 < 9^9