Question

Chứng minh:

\(\frac{1}{3}+\frac{1}{31}+\frac{1}{35}+\frac{1}{37}+\frac{1}{47}+\frac{1}{53}+\frac{1}{61}< \frac{1}{2}\)

 

Answer 1

không biết ?

Answer 2

Ta thấy:  \(\frac{1}{31}+\frac{1}{35}+\frac{1}{37}< \frac{1}{30}\)

               \(\frac{1}{37}< \frac{1}{35}< \frac{1}{31}< \frac{1}{30}\)

               \(\frac{1}{47}+\frac{1}{53}+\frac{1}{61}< \frac{1}{45}\)

               \(\frac{1}{61}< \frac{1}{53}< \frac{1}{47}< \frac{1}{45}\)

Do đó:   \(\frac{1}{3}+\frac{1}{31}+\frac{1}{35}+\frac{1}{37}+\frac{1}{47}+\frac{1}{53}+\frac{1}{61}< \frac{1}{3}+\frac{1}{30}\cdot3+\frac{1}{45}\cdot3=\frac{1}{2}\)