Question

CMR

\(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+.......+\frac{1}{19}>1\)

Answer 1

Vì \(\frac{1}{4}>\frac{1}{16};\frac{1}{5}>\frac{1}{16};...;\frac{1}{19}>\frac{1}{16}\)

\(\Rightarrow\)\(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+.....+\frac{1}{19}>\frac{1}{16}+\frac{1}{16}+.....+\frac{1}{16}\) ( 16 số)

                                                            \(=\frac{1+1+1+.....+1}{16}\)

                                                            \(=\frac{16}{16}=1\)

Vậy: \(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+.....+\frac{1}{19}>1\)

Answer 2

\(\frac{1}{13}x14=\frac{14}{13}>1\)

Answer 3

Ta có: 1/4 + 1/5 + 1/6 +.....+ 1/19 > 1/4 + ( 1/20 + 1/20 + .......) ( có 15 p/s 1/20) = 1/4 + 3/4 = 1

Vậy 1/4 + 1/5 + 1/6 + ...... + 1/19 > 1

Answer 4

đặt \(B=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}>1\)

\(B=\frac{1}{4}+\left(\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}\right)>\frac{1}{4}+15\cdot\frac{1}{20}\)

\(B>\frac{1}{4}+\frac{15}{20}=\frac{1}{4}+\frac{3}{4}=1\)

\(\Rightarrow B>1\)

CHẮC SIA

Answer 5

Đặt B = 1/4 + 1/5 + 1/6 + ... + 1/19 > 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