Question

so sánh \(\frac{178}{179}+\frac{179}{180}+\frac{183}{181}\)với 3

Answer 1

Ta có \(\frac{178}{179}+\frac{179}{180}+\frac{183}{181}=\left(1-\frac{1}{179}\right)+\left(1-\frac{1}{180}\right)+\left(1+\frac{2}{181}\right)\)

\(=3-\left(\frac{1}{179}-\frac{1}{180}+\frac{2}{181}\right)\)

Ta thấy \(\frac{1}{179}-\frac{1}{180}+\frac{2}{181}>0\)suy ra \(3-\left(\frac{1}{179}-\frac{1}{180}+\frac{2}{181}\right)< 3\)

Khi đó \(\frac{178}{179}+\frac{179}{180}+\frac{183}{181}< 3\)