Cho 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 / 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)
Cho B=1/4+1/5+1/6+1/7+....+1/19. Chứng tỏ B>1.
Cho: 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 rằng B>1
Xét: 1 / 4 > 1 / 16 ; 1 / 5 > 1 / 16
=) 1 / 4 + 1 / 5 + 1 / 6 + ... + 1 / 19 > 16 . 1 / 16 = 16 /16 = 1
=) B > 1
Vậy B > 1
B= 1/4+(1/5+1/6+...+1/9)+(1/10+1/11+...+1/19)
Vì 1/5+1/6+...+1/9 > 1/9+1/9+...+1/9 nên 1/5+1/6+...+1/9 > 5/9 >1/2
Vì 1/10+1/11+...+1/19 > 1/19+1/19+...+1/19 nên 1/10+1/11+...+1/19 > 10/19 >1/2
Suy ra: B > 1/4+1/2+1/2 > 1
cho 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 rằng B>1.
B = 1/4 + 1/5 + 1/6 +....+1/19
> 1/4 + ( 1/20 + 1/20 +.....+1/20) ( 15 p/s 1/20) = 1/4 + 3/4 = 1
=> B > 1
Vậy B > 1
cho B = 1/4+1/5+1/6 +....+1/19.hãy chứng tỏ rằng B > 1
Ta có :
\(B=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}\)
\(B=\frac{1}{4}+\left(\frac{1}{5}+\frac{1}{6}+...+\frac{1}{9}\right)+\left(\frac{1}{10}+\frac{1}{11}+...+\frac{1}{19}\right)\)
Vì \(\frac{1}{5}+\frac{1}{6}+...+\frac{1}{9}>\frac{1}{9}+\frac{1}{9}+...+\frac{1}{9}=\frac{5}{9}>\frac{1}{2}\)
Vì \(\frac{1}{10}+\frac{1}{11}+...+\frac{1}{19}>\frac{1}{19}+\frac{1}{19}+...+\frac{1}{19}=\frac{10}{19}>\frac{1}{2}\)
\(\Rightarrow B>\frac{1}{4}+\frac{5}{9}+\frac{10}{19}>\frac{1}{4}+\frac{1}{2}+\frac{1}{2}>1\)
\(\Rightarrow B>1\)
\(B=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}\)
\(\Rightarrow B=\left(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}\right)+\left(\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}\right)+\left(\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}\right)\)Do \(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}>\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}\)
\(\Rightarrow\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}>4.\frac{1}{8}=\frac{1}{2}\left(1\right)\)
\(\Rightarrow\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}>4.\frac{1}{12}=\frac{1}{3}\left(2\right)\)
\(\Rightarrow\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}>4.\frac{1}{16}=\frac{1}{4}\left(3\right)\)
\(\Rightarrow\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}>4.\frac{1}{20}=\frac{1}{5}\left(4\right)\)
Từ (1) , ( 2 ) , ( 3 ) và ( 4 ) suy ra :
\(B>\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\)
\(B>\frac{1}{2}+\frac{1}{4}+\frac{1}{4}+\frac{1}{5}\)
\(B>\frac{1}{2}+\frac{1}{2}+\frac{1}{5}\)
\(B>1+\frac{1}{5}\Rightarrow B>1\)
Vậy : \(B>1\)