giúp mới mình sẽ tích

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ai nhanh nhất mình sẽ cho 3 k

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

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

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

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

   \(=\frac{2015.2}{2016}\)

    \(=...\)(tự tinhs)

\(=\frac{4}{3}.\frac{9}{8}...\frac{4060225}{4060224}\)

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

\(=\frac{2.2.3.3...2015.2015}{1.3.2.4...2014.2016}\)

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

\(=2015.\frac{2}{2016}\)

\(=2015.\frac{1}{1008}\)

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

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

\(=\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}...\frac{2015.2015}{2014.2016}\)

\(=\frac{2.2.3.3.4.4...2015.2015}{1.3.2.4.3.5...2014.2016}\)

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

\(=\frac{2015.2}{2016}=\frac{2015}{1008}\)

Vậy \(C=\frac{2015}{1008}\)

2015/2016

C=\(\frac{2015}{1008}\)

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