Question

so sánh A với 1/2 biết A = ( 1-1/2*2)* (1-1/3*3) * ( 1-1/4*4)* ...* ( 1-1/2016*2016)

Answer 1

A=\(\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}.....\frac{2016^2-1}{2016^2}\)

A=\(\frac{\left(2+1\right)\left(2-1\right)}{2^2}.\frac{\left(3+1\right)\left(3-1\right)}{3^2}......\frac{\left(2016+1\right)\left(2016-1\right)}{2016^2}\)

A=\(\frac{3.4......2017}{2.3....2016}.\frac{1.2...2015}{2.3...2016}\)

A=\(\frac{2017}{2}.\frac{1}{2016}\)

A=\(\frac{2017}{2.2106}>\frac{1}{2}\)

Vậy A\(>\frac{1}{2}\)