cho \(A=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{60}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\)\(\frac{1}{63}\)
chứng minh \(A< \frac{1}{2}\)
ai làm nhanh,đúng sẽ được 1 like
Chứng minh rằng \(S=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}
Ta có : \(S=\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)
Ta có:
\(S=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\)
\(=\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)\)
Bài toán phụ 1:
Ta có:
1/13<1/12
1/14<1/12
1/15<1/12
=>1/13+1/14+1/15<1/12x3=1/4 (1)
Bài toán phụ 2:
Ta có:
1/61<1/60
1/62<1/60
1/63<1/60
=>1/61+1/62+1/63<1/60x3=1/20 (2)
Từ (1) và (2), ta có:
1/5+1/13+1/14+1/15+1/61+1/62+1/63<1/5+1/4+1/20
1/5+1/13+1/14+1/15+1/61+1/62+1/63<4/20+5/20+1/20
1/5+1/13+1/14+1/15+1/61+1/62+1/63<9/20<1/2
=>1/5+1/13+1/14+1/15+1/61+1/62+1/63<1/2
Chung to A=\(\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}<\frac{1}{2}\)
so sánh D với 1 phần 2:
D=\(\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\)
Ta có :
\(\frac{1}{13}< \frac{1}{12};\frac{1}{14}< \frac{1}{12};\frac{1}{15}< \frac{1}{12}\Rightarrow\frac{1}{13}+\frac{1}{14}+\frac{1}{15}< \frac{1}{12}+\frac{1}{12}+\frac{1}{12}=\frac{1}{4}\)
\(\frac{1}{61}< \frac{1}{60};\frac{1}{62}< \frac{1}{60};\frac{1}{63}< \frac{1}{60}\Rightarrow\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{60}+\frac{1}{60}+\frac{1}{60}=\frac{1}{20}\)
\(\Rightarrow D=\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)< \frac{1}{5}+\frac{1}{4}+\frac{1}{20}=\frac{1}{2}\)
Vậy \(D< \frac{1}{2}\)
\(D=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}=\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)\)
Nhận xét: \(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}< \frac{1}{12}+\frac{1}{12}+\frac{1}{12}=\frac{3}{12}=\frac{1}{4}\)
\(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{60}+\frac{1}{60}+\frac{1}{60}=\frac{3}{60}=\frac{1}{20}\)
\(\Rightarrow D< \frac{1}{5}+\frac{1}{4}+\frac{1}{20}=\frac{1}{2}\)
Vậy D < 1/2
Cho S=\(\frac{1}{5}\)+\(\frac{1}{13}\)+\(\frac{1}{14}\)+\(\frac{1}{15}\)+\(\frac{1}{61}\)+\(\frac{1}{62}\)+\(\frac{1}{63}\)
Chứng minh S<\(\frac{1}{2}\)
Ai học lớp 6 trở lên mà ko làm được thì về Tiểu học học lại.
Ta có :
\(\frac{1}{13}< \frac{1}{12}\)
\(\frac{1}{14}< \frac{1}{12}\)
\(\frac{1}{15}< \frac{1}{12}\)
\(\Rightarrow\frac{1}{13}+\frac{1}{14}+\frac{1}{15}< \frac{1}{12}+\frac{1}{12}+\frac{1}{12}=3\cdot\frac{1}{12}=\frac{1}{4}\) (1)
Ta cũng có :
\(\frac{1}{61}< \frac{1}{60}\)
\(\frac{1}{62}< \frac{1}{60}\)
\(\frac{1}{63}< \frac{1}{60}\)
\(\Rightarrow\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{60}+\frac{1}{60}+\frac{1}{60}=3\cdot\frac{1}{60}=\frac{1}{20}\) (2)
Từ (1) ; (2) \(\Rightarrow S=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{5}+\frac{1}{4}+\frac{1}{20}=\frac{1}{2}\)
=> S < \(\frac{1}{2}\) (đpcm)
Chứng minh :
\(S=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\)< \(\frac{1}{2}\)
S=1/5+(1/13+1/14+1/15)+(1/61+1/62+1/63)
suy ra S<1/5+1/12.3+1/60.3
S<1/5+1/4+1/20
S<1/2
Dãy số này không viết theo qui luật nên bạn chỉ có cách là cộng tất cả các số hạng vào rồi xét nó bé hơn \(\frac{1}{2}\)
câu trả lời của bạn lê phương thảo đúng rồi
chứng minh rằng:a/ \(\frac{1}{4}+\frac{1}{16}+\frac{1}{36}+\frac{1}{64}+\frac{1}{100}+\frac{1}{144}+\frac{1}{196}< \frac{1}{2}\) \(\frac{1}{2}\)
b/\(\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{2}\)\(\frac{1}{2}\)
nhanh thì tích
chậm thì thôi
So sánh \(A=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\)VÀ \(B=\frac{1}{2}\)
\(A=\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)
chứng minh: S= \(\frac{1}{5}\)+\(\frac{1}{13}\)+\(\frac{1}{14}\)+\(\frac{1}{15}\)+\(\frac{1}{61}\)+\(\frac{1}{62}\)+\(\frac{1}{63}\)<\(\frac{1}{2}\)
Chứng minh : S = \(\frac{1}{5}\)+ \(\frac{1}{13}\)+ \(\frac{1}{14}\)+ \(\frac{1}{15}\)+ \(\frac{1}{61}\)+\(\frac{1}{62}\)+\(\frac{1}{63}\)<\(\frac{1}{2}\)
Lấy máy tính bấn tổng kia thì bé hơn 1/2. Xem lại đề