b+1/4+1/5+1/6+...+1/19
chứng tỏ b>1
Cho B = 1/4+1/5+1/6+....+1/19. Hãy chứng tỏ B > 1
B=(1/4+1/5+1/6+1/7)+...+(1/16+1/17+1/18+1/19)
1/4+1/5+1/6+1/7>4*1/7=4/7
1/8+1/9+1/10+1/11>4*1/11=4/11
...
1/16+1/17+1/19+1/19>4/19
=>B>4(1/7+1/11+1/15+1/19)>1
cho B=1/4+1/5+1/6+1/7+1/8+...+1/15
Chứng tỏ B<2
cho B = 1/4 + 1/5 + 1/6 + ... + 1 / 19 . Hãy chứng tỏ rằng B>1
b=1/4+1/5+1/6+...+1/19. chứng tỏ b>1 ?
B=1/4+1/5+1/6+...+1/19 Chưng tỏ rằng B>1
Ta có :
\(B=\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...........+\dfrac{1}{19}\)
\(B=\dfrac{1}{4}+\left(\dfrac{1}{5}+\dfrac{1}{6}+......+\dfrac{1}{9}\right)+\left(\dfrac{1}{10}+\dfrac{1}{11}+..........+\dfrac{1}{19}\right)\)
Ta thấy :
\(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}>\dfrac{1}{9}+\dfrac{1}{9}+\dfrac{1}{9}+\dfrac{1}{9}+\dfrac{1}{9}\)\(=\dfrac{1}{9}.5=\dfrac{5}{9}\)\(>\dfrac{1}{2}\)
\(\dfrac{1}{10}+\dfrac{1}{11}+\dfrac{1}{12}+......+\dfrac{1}{19}>\dfrac{1}{19}+\dfrac{1}{19}+.........+\dfrac{1}{19}\)\(=\dfrac{1}{19}.5=\dfrac{5}{19}\)\(>\dfrac{1}{2}\)
\(\Rightarrow B>\dfrac{1}{4}+\dfrac{1}{2}+\dfrac{1}{2}=\dfrac{5}{4}>1\)
\(\Rightarrow B>1\rightarrowđpcm\)
~ Chúc bn học tốt ~
Cho B=1/4+1/5+1/6+1/7+....+1/19. Chứng tỏ B>1.
B=1/4+1/5+1/6+...+1/19.Hãy chứng tỏ rằng B>1
Cho B = 1/4+1/5+1/6+.......+1/19.Hãy chứng tỏ B >1
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B=1/4+1/5+1/6+...+1/19
⇒B>1/4+1/19+1/19+1/19+...+1/19 có 15 số 1/19
⇒B>1/4+15.1/19
⇒B>1/4+15/19
⇒B>19/76+60/76
⇒B>79/76>1
⇒B>1 (đpcm)
b =1/4+1/5+1/6+...+1/19 hãy chứng tỏ rằng b>1