Question

chứng minh \(\frac{2}{3^2}\)+ \(\frac{2}{4^2}\)+ \(\frac{2}{5^2}\) + ..... + \(\frac{2}{2016^2}\)< 1

Answer 1

2/3² + 2/4² + 2/5² + ... + 2/2016² < 2/2.3 + 2/3.4 + 2/4.5 + ... + 2/2015.2016

< 2.(1/2.3 + 1/3.4 + 1/4.5 + ... + 1/2015.2016)

< 2.(1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/2015 - 1/2016)

< 2.(1/2 - 1/2016)

< 2.1/2 = 1

=> đpcm

Answer 2

sao 2.(1/2 - 1/2016) = 2.1/2 vậy bạn