\(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+....+\frac{4031}{2015^2.2016^2}=\frac{1}{1^2}-\frac{1}{2^2}+\frac{1}{2^2}-.....-\frac{1}{2016^2}=1-\frac{1}{2016^2}\)
\(\frac{1}{2016^2}>0\Rightarrow A< 1\left(ĐPCM\right)\)
bạn chờ xíu mk lm câu sau nha
\(Taco:\)
\(\frac{x}{x+y}+\frac{y}{y+z}+\frac{z}{z+x};x,y,z\inℕ^∗\)
\(\frac{x}{x+y}+\frac{y}{y+z}+\frac{z}{z+x}>\frac{x}{x+y+z}+\frac{y}{x+y+z}+\frac{z}{x+y+z}=1\)
\(\Rightarrow P>1\)
Giả sử: \(x>y>z\)
\(\Rightarrow\frac{y}{y+z}+\frac{z}{z+x}< \frac{x+y}{y+z}=1;\frac{x}{x+y}< 1\Rightarrow P< 1+1=2\Rightarrow1< P< 2\left(ĐPCM\right)\)