Question

[Đoàn Bá Quý]

các bạn ơi giúp mình với .Chứng minh rằng:1/2²+1/4² +1/6²+........+1/2016²<1/2

Answer 1

[shitbo]

Toi mk lm cho

Answer 2

[Ahwi]

\(\text{đặt }A=\frac{1}{2^2}+\frac{1}{4^2}+\frac{1}{6^2}+...+\frac{1}{2016^2}\)

\(A=\frac{1}{2^2}.\left(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+....+\frac{1}{1008^2}\right)\)

\(A< \frac{1}{2^2}.\left(\frac{1}{1}+\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{1007.1008}\right)\)

\(A< \frac{1}{4}.\left(1+1-\frac{1}{2007}\right)< \frac{1}{4}.2=\frac{1}{2}\Rightarrow A< \frac{1}{2}\left(ĐPCM\right)\)