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29 tháng 4 2017

\(\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right)....\left(1+\frac{1}{2014.2015}\right)\)

\(\left(1.3+\frac{1}{1.3}\right)...\left(2014.2015+\frac{1}{2014.2015}\right)\)

\(\left(\frac{2.2}{1.3}\right)...\left(\frac{2015.2015}{2014.2015}\right)\)

\(\frac{\left(2...2015\right).\left(2...2015\right)}{\left(1.2....2014\right).\left(3...2015\right)}\)

\(\frac{2015.2}{2015}=\frac{2015.2}{1007,5.2}=\frac{2015}{1007.5}=2\)

đúng 100%

29 tháng 4 2017

\(C=\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)..........\left(1+\frac{1}{2014.2016}\right)\)

\(=\frac{2^2}{1.3}.\frac{3^2}{2.4}..........\frac{2015^2}{2014.2016}\)

\(=\frac{2^2.3^2............2015^2}{\left(1.3\right)\left(2.4\right).......\left(2014.2016\right)}\)

\(=\frac{\left(2.3......2015\right)\left(2.3.......2015\right)}{\left(1.2.....2014\right)\left(3.4.......2016\right)}\)

\(=\frac{2.2015}{1.2016}=\frac{2015}{1008}\)

13 tháng 2 2018

\(B=2016.\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{2014.2016}\right)\)

\(2016.\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}....\frac{2015^2}{2014.2016}\)

\(2016.\frac{2.3.4....2015}{1.2.3.4.5...2014.2015.2016}.\frac{2.3.4....2015}{3.4.5...2014}\)

\(2016.\frac{1}{2016}.2.2015=2.2015=4030\)

6 tháng 4 2022

\(C=\left(1+\frac{1}{1.3}\right)\)\(.\left(1+\frac{1}{2.4}\right)\)\(.\left(1+\frac{1}{3.5}\right)\)\(.\left(1+\frac{1}{2014.2016}\right)\)

   \(=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...\frac{2015^2}{2014.2016}\)

   \(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}...\frac{2015.2015}{2014.2016}\)

   \(=\frac{\left(2.3.4...2015\right).\left(2.3.4...2015\right)}{\left(1.2.3...2014\right).\left(3.4.5...2016\right)}\)

   \(=\frac{2015.2}{2016}\)

    \(=...\)(tự tinhs)

19 tháng 10 2023

\(C=\dfrac{4}{1.3}.\dfrac{9}{2.4}.\dfrac{16}{3.5}.\dfrac{25}{4.6}....\dfrac{9801}{9800}=\)

\(=\dfrac{2^2.3^2.4^2.5^2.....99^2}{1.2.3^2.4^2.5^2....98^2.99.100}=\dfrac{2.99}{100}=\dfrac{198}{100}=1,98\)

16 tháng 4 2016

ket qua la 5435 ban nha