Find the smallest \(a,b\) so that \(a^7=b^8\)
Find 2 fraction that their numberator is 1 and their sum are equals to \(\dfrac{1}{4}\) (Find 2 pairs)
Find 2 positive number so that the product of them are double than their sum (Find 2 pairs)
Find a 4-digit positive number \(abcd\) given:
\(a^a+\left[b,c,d\right]=100\)
Give a,b,c are different pair-one prime numbers.
Prove that: \(\dfrac{1}{\left[a,b\right]}+\dfrac{1}{\left[b,c\right]}+\dfrac{1}{\left[a,c\right]}\le\dfrac{1}{3}\)
Prove that:
\(\dfrac{1}{2!}+\dfrac{1}{3!}+...+\dfrac{1}{100!}< 1\)
\(\dfrac{3}{4}+\dfrac{8}{9}+\dfrac{15}{16}+...+\dfrac{2499}{2500}>48\)
\(\dfrac{1}{3}+\dfrac{1}{31}+\dfrac{1}{35}+\dfrac{1}{37}+\dfrac{1}{47}+\dfrac{1}{53}+\dfrac{1}{61}< \dfrac{1}{2}\)
The price of 1 book, 6 notebooks and 3 pens are 7700 VNĐ. The price of 8 books, 6 notebooks and 6 pens are 16000 VNĐ. Compare the price of 1 book and 1 notebook.
Compare:
\(A=1.2.3...20\) with \(B=1+2+3+...+1000000\)
\(A=1+2+3+...+1000\) with \(B=1.2.3...11\)
Calculate:
\(1.2.3+2.3.4+3.4.5+...+98.99.100\) and \(1.2.3.4+2.3.4.5+...+27.28.29.30\)
\(\dfrac{2n+1}{4n+3};\dfrac{4n+1}{12n+7}and\dfrac{7n+4}{9n+5}\) divisible by \(d=1;-1\)
\(\dfrac{2.4+2.4.8+4.8.16+8.16.32}{3.4+2.6.8+4.12.16+8.24.32}
Find \(x\) so that:
a) \(A\) has a value of an integer number.
b) \(A\) has the largest value.
\(A=\dfrac{x+5}{x+2}\)
\(\dfrac{17}{21}\) and \(\dfrac{17171}{21211}\)
\(\dfrac{10^{2016}+1}{10^{2017}+1}\) and \(\dfrac{10^{2015}+1}{10^{2016}+1}\)
If \(bd>0\) then \(\dfrac{a}{b}>\dfrac{c}{d}\) only when \(ad>bc\).
What is the smallest common denominator of:
\(\dfrac{2^{10}.9^6}{4^6.3^{11}}\) ; \(\dfrac{6^{12}}{9^5.2^{14}}\) and \(\dfrac{15^5.2^6.3^3}{5^6.6^8}\)
\(\dfrac{xy-x^2}{y^2-xy}=\dfrac{x}{y}\)