Find a,b,c \(\left(a,b,c\ne\right)\) so that:
\(a,bc:\left(a+b+c\right)=0,25\)
Find a,b such that:
\(\dfrac{a}{2}+\dfrac{b}{3}=\dfrac{a+b}{2+3}\)
Calculate:
\(\dfrac{8}{9}.\dfrac{15}{16}.\dfrac{24}{25}...\dfrac{2499}{2500}\)
\(\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{6}\right)\left(1-\dfrac{1}{10}\right)\left(1-\dfrac{1}{15}\right)...\left(1-\dfrac{1}{780}\right)\)
\(\left(\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{100}\right):\left(\dfrac{1}{1.2}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\right)\)
Prove that:
\(\left(1+\dfrac{1}{3}+\dfrac{1}{5}+...+\dfrac{1}{99}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{100}\right)=\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{100}\)
Calculate \(\dfrac{A}{B}\) :
\(A=\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{200}\)
\(B=\dfrac{1}{199}+\dfrac{2}{198}+...+\dfrac{198}{2}+\dfrac{199}{1}\)
\(A=\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{10}}\)
Find the value of x:
\(\dfrac{1}{5.8}+\dfrac{1}{8.11}+...+\dfrac{1}{x\left(x+3\right)}=\dfrac{101}{1540}\)
Prove that the sum of 100 fraction in the series is smaller than \(\dfrac{1}{4}\):
\(\dfrac{1}{5},\dfrac{1}{45},\dfrac{1}{117}...\)
\(A=\dfrac{1}{1.300}+\dfrac{1}{2.301}+...+\dfrac{1}{101.400}\)
\(B=\dfrac{1}{1.102}+\dfrac{1}{2.103}+...+\dfrac{1}{299.400}\)
Compact:
\(\dfrac{121212}{424242}\) ; \(\dfrac{187187187}{221221221}\) and \(\dfrac{3.7.13.37.39-10101}{505050+70707}\)
\(181-\left\{-85+\left[220+\left(-65-35\right)\right]\right\}\)
Find 2 fractions have their denominator are 21 satisfy: \(\dfrac{-5}{6}< \dfrac{x}{21}< \dfrac{-5}{7}\)
Use all ten digits from 0 to 9, write:
+ The smallest number divisible by 4.
+ The biggest number divisible by 4.
Prove that: \(2^{100}\) is a number that has 31 digits when we write the number in decimal system.
When we write the result of \(4^{50}and25^{50}\) continuously, we get a number that has how many digits?
Find x satisfy:
\(\dfrac{4}{11}< \dfrac{x}{20}< \dfrac{5}{11}\)
Compare:
\(\dfrac{10^7+5}{10^7-8}and\dfrac{10^8+6}{10^8-7}\)
\(\dfrac{3}{8^3}+\dfrac{7}{8^4}and\dfrac{7}{8^3}+\dfrac{3}{8^4}\)