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Ta thấy:
1/11<1/4
1/12<1/4
.......
1/20<1/4
Suy ra ta có:
\(S=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+....+\frac{1}{20}\)
\(=\left(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}\right)\)
\(>\frac{1}{15}\cdot5+\frac{1}{20}\cdot5\)
\(=\frac{1}{3}+\frac{1}{4}\)
\(=\frac{7}{12}>\frac{6}{12}=\frac{1}{2}\)
\(\Rightarrow S>\frac{1}{2}\)
Bài làm
Ta có:
\(\frac{1}{11}>\frac{1}{20}\), \(\frac{1}{12}>\frac{1}{20}\), \(\frac{1}{13}>\frac{1}{20}\), \(\frac{1}{14}>\frac{1}{20}\), \(\frac{1}{15}>\frac{1}{20}\), \(\frac{1}{16}>\frac{1}{20}\), \(\frac{1}{17}>\frac{1}{20}\), \(\frac{1}{18}>\frac{1}{20}\),\(\frac{1}{19}>\frac{1}{20}\)
=> \(S=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}>\frac{1}{20}\)
hay \(\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}\)
=> \(S=\frac{1}{20}.10=\frac{10}{20}=\frac{1}{2}\)
Do đó: \(S=\frac{1}{2}\)
# Chúc bạn học tốt #
Đặt S=1/12+1/13+1/14+1/15+...+1/23
ta có 1/12+1/13+1/14+1/15+...+1/22+1/23 = (1/12+1/13+1/14+...+1/17)+(1/18+1/19+...+1/23)
đặt A=1/12+1/13+1/14+...+1/17
ta có
1/13<1/12
1/14<1/12
..........................
.........................
1/17<1/12
=>A<1/12+1/12+1/12+....+1/12 (có 6 phân số)
=>A<1x6/12
=>A<1/2 (1)
Đặt B=1/18+1/19+...+11/23
ta có
1/19<1/18
1/20<1/18
...........................
..........................
1/23<1/18
=> B<1/18+1/18+1/18+...+1/18 (có 6 phân số)
=>B<1x 6/18
=>B<1/3 (2)
từ 1 và 2 =>S=A+B<1/2+1/3
=>S<5/6 (dpcm)
k cho mình nhé
Đặt S=1/12+1/13+1/14+1/15+...+1/23
ta có 1/12+1/13+1/14+1/15+...+1/22+1/23 = (1/12+1/13+1/14+...+1/17)+(1/18+1/19+...+1/23)
đặt A=1/12+1/13+1/14+...+1/17
ta có
1/13<1/12
1/14<1/12
..........................
.........................
1/17<1/12
=>A<1/12+1/12+1/12+....+1/12 (có 6 phân số)
=>A<1x6/12
=>A<1/2 (1)
Đặt B=1/18+1/19+...+11/23
ta có
1/19<1/18
1/20<1/18
...........................
..........................
1/23<1/18
=> B<1/18+1/18+1/18+...+1/18 (có 6 phân số)
=>B<1x 6/18
=>B<1/3 (2)
từ 1 và 2 =>S=A+B<1/2+1/3
=>S<5/6 (dpcm)
k cho mình nhé
\(A\)\(=\)\(\frac{1}{9}\)\(-\)\(\frac{1}{10}\)\(+\)\(\frac{1}{10}\)\(-\)\(\frac{1}{11}\)\(+\)\(\frac{1}{11}\)\(-\)\(\frac{1}{12}\)\(+\)\(\frac{1}{12}\)\(-\)\(\frac{1}{13}\)\(+\)\(\frac{1}{13}\)\(-\)\(\frac{1}{14}\)\(+\)\(\frac{1}{14}\)\(-\)\(\frac{1}{15}\)
\(A\)\(=\)\(\frac{1}{9}\)\(-\)\(\frac{1}{15}\)
\(A\)\(=\)\(\frac{2}{45}\)
\(A=\left(\frac{1}{9}.\frac{1}{10}+\frac{1}{10}.\frac{1}{11}\right)+\left(\frac{1}{11}.\frac{1}{12}+\frac{1}{12}.\frac{1}{13}\right)+\left(\frac{1}{13}.\frac{1}{14}+\frac{1}{14}.\frac{1}{15}\right)\)
Sau đó nhân phân phối ra là xong nhé bạn
em mới học lớp 5 à