M = \(\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right).....\left(1-\frac{1}{2015^2}\right)\)
M = \(\left(-\frac{1.3}{2.2}\right)\left(-\frac{2.4}{3.3}\right)\left(-\frac{3.5}{4.4}\right)....\left(-\frac{2014.2016}{2015.2015}\right)\)
M = \(\frac{\left(1.2.3....2014\right)\left(3.4.5...2016\right)}{\left(2.3.4.....2015\right)\left(2.3.4....2015\right)}\)
M = \(\frac{2016}{2015.2}\)
M = \(\frac{1008}{2015}\)
N = \(\frac{1}{2}\)=\(\frac{1008}{2016}\)
Vì \(\frac{1008}{2015}>\frac{1008}{2016}\)
=> M > N
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