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\(\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right)....\left(1+\frac{1}{2014.2015}\right)\)
\(\left(1.3+\frac{1}{1.3}\right)...\left(2014.2015+\frac{1}{2014.2015}\right)\)
\(\left(\frac{2.2}{1.3}\right)...\left(\frac{2015.2015}{2014.2015}\right)\)
\(\frac{\left(2...2015\right).\left(2...2015\right)}{\left(1.2....2014\right).\left(3...2015\right)}\)
\(\frac{2015.2}{2015}=\frac{2015.2}{1007,5.2}=\frac{2015}{1007.5}=2\)
đúng 100%
\(C=\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)..........\left(1+\frac{1}{2014.2016}\right)\)
\(=\frac{2^2}{1.3}.\frac{3^2}{2.4}..........\frac{2015^2}{2014.2016}\)
\(=\frac{2^2.3^2............2015^2}{\left(1.3\right)\left(2.4\right).......\left(2014.2016\right)}\)
\(=\frac{\left(2.3......2015\right)\left(2.3.......2015\right)}{\left(1.2.....2014\right)\left(3.4.......2016\right)}\)
\(=\frac{2.2015}{1.2016}=\frac{2015}{1008}\)
\(5^x=125\)
\(5^x=5^3\)
=> x=3 ( vì cơ số 5>1)
\(3^2.x=81\)
\(9x=81\)
\(x=81:9\)
\(x=9\)