Question

B=\(\frac{1}{4}+\frac{1}{5}+....+\frac{1}{19}\)

Chứng tỏ B > 1

Answer 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
 

Answer 2

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
 

Answer 3

Tách : \(A=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{11}\)( 8 số hạng )

\(C=\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+...+\frac{1}{19}\)( 8 số hạng )

Nhận thấy : \(A=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{11}>\frac{1}{11}.8=\frac{8}{11}\)

\(C=\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+...+\frac{1}{19}>\frac{1}{19}.8=\frac{8}{19}\)

\(\Rightarrow\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}>\frac{8}{19}+\frac{8}{11}=\frac{240}{209}>1\)

\(\Rightarrow B>1\)