Question

Bo sánh các biểu thức sau: A = 1/21 + 1/22 + 1/23 + ... + 1/50 và B = 3/4

Answer 1

Ta có: \(\dfrac{1}{21}+\dfrac{1}{22}+...+\dfrac{1}{50}< \dfrac{1}{60}\times30\)

\(\dfrac{1}{21}+\dfrac{1}{22}+...+\dfrac{1}{50}< \dfrac{1}{2}< \dfrac{3}{4}\)(đpcm)

 

Answer 2

Lời giải:

$\frac{1}{21}+\frac{1}{22}+...+\frac{1}{30}> \frac{1}{30}+\frac{1}{30}+...+\frac{1}{30}=\frac{10}{30}=\frac{1}{3}$

$\frac{1}{31}+\frac{1}{32}+...+\frac{1}{40}> \frac{10}{40}=\frac{1}{4}$
$\frac{1}{41}+\frac{1}{42}+....+\frac{1}{50}> \frac{10}{50}=\frac{1}{5}$

Cộng lại:

$A> \frac{1}{3}+\frac{1}{4}+\frac{1}{5}$

$A> \frac{47}{60}> \frac{3}{4}$