Question

Chứng minh : \(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{9}< 2\)

Giúp mình nha

Answer 1

Ta có:

\(\dfrac{1}{2}\) < 1

\(\dfrac{1}{3}\) < 1

\(\dfrac{1}{4}\) <1

...

\(\dfrac{1}{9}\) < 1

=> \(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{9}\) < 1 < 2

Vậy \(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{9}\) < 2

Answer 2

Ta có 1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9=1.82<2