Chứng minh rằng : 1/5 + 1/14 + 1/28 + 1/44 + 1/61 + 1/85 < 1/2
chứng minh rằng 1/5+1/14+1/28+1/44+1/61+1/85+1/91<1/2
Chứng minh rằng : 1/5 + 1/14 + 1/28 + 1/44 + 1/61 + 1/85 + 1/91 < 1/2
1/97 chứ sao lại 1/91!
giải:
đặt :1/5+1/14+1/28+1/44+1/61+1/85+1/97 =A
ta có :A=1/5(1/14+1/28+1/44)+(1/61+1/85+1/97)
A<1/5(1/14.3)+(1/61.3)
A<1/5+3/14+3/61
A<1/5+3/12+1/20
A<1/5+1/4+1/20
=>A<1/2
VẬY dpcm
chứng minh rằng 1/5+1/14+1/28+1/44+1/61+1/85+1/91<1/2
B=1/5+1/14+1/28+1/44+1/61+1/85 Chứng minh rằng B<1/2
Cách 1: Tính hết kết quả vế trái là so sánh được => đpcm
Cách 2: Ta đánh giá: Cho a, b là 2 số dương nếu a < b thì 1/a > 1/b
Vậy:
VT < 1/5 + 1/14 + 1/14 + 1/14 + 1/14 + 1/14
= 1/5 + 5/14 = (14 + 25)/(5.14) = 39/70 < 1 (đpcm)
Có thể còn cách khác, bạn tìm thêm đi.
chứng minh: 1/5 + 1/14+1/28 +1/44 + 1/61+1/85+1/97 <1/2
chứng minh
1/5+1/14+1/28+1/44+1/61+1/85+1/97<1/2
Chứng minh rằng:
\(\dfrac{1}{5}-\dfrac{1}{14}+\dfrac{1}{28}+\dfrac{1}{44}+\dfrac{1}{61}+\dfrac{1}{85}+\dfrac{1}{97}< \dfrac{1}{2}\)
Sai đề. Sửa đề :v
Cmr: \(\dfrac{1}{5}+\dfrac{1}{14}+\dfrac{1}{28}+\dfrac{1}{44}+\dfrac{1}{61}+\dfrac{1}{85}+\dfrac{1}{97}< \dfrac{1}{2}\)
Giải:
Đặt \(A=\dfrac{1}{5}+\dfrac{1}{14}+\dfrac{1}{28}+\dfrac{1}{44}+\dfrac{1}{61}+\dfrac{1}{85}+\dfrac{1}{97}\)
Ta có:
\(A=\dfrac{1}{5}+\left(\dfrac{1}{14}+\dfrac{1}{28}+\dfrac{1}{44}\right)+\left(\dfrac{1}{61}+\dfrac{1}{85}+\dfrac{1}{97}\right)\)
\(A< \dfrac{1}{5}\left(\dfrac{1}{14.3}\right)+\left(\dfrac{1}{61.3}\right)\)
\(A< \dfrac{1}{5}+\dfrac{3}{14}+\dfrac{3}{61}\)
\(A< \dfrac{1}{5}+\dfrac{3}{12}+\dfrac{1}{20}\)
\(A< \dfrac{1}{5}+\dfrac{1}{4}+\dfrac{1}{20}\)
\(\Rightarrow A< \dfrac{1}{2}\)
Vậy \(\dfrac{1}{5}+\dfrac{1}{14}+\dfrac{1}{28}+\dfrac{1}{44}+\dfrac{1}{61}+\dfrac{1}{85}+\dfrac{1}{97}< \dfrac{1}{2}\) \((đpcm)\)
chứng tỏ rằng
A= 1/5 + 1/14 + 1/28 + 1/44 + 1/61 + 1/85 + 1/97 < 1/2
Ta có \(\frac{1}{5}=\frac{1}{5}\)
\(\frac{1}{14}< \frac{1}{10};\frac{1}{28}< \frac{1}{10}\)
\(\frac{1}{44}< \frac{1}{40};\frac{1}{61}< \frac{1}{40};\frac{1}{85}< \frac{1}{40};\frac{1}{97}< \frac{1}{40}\)
\(\Rightarrow\frac{1}{5}+\frac{1}{14}+\frac{1}{28}+\frac{1}{44}+\frac{1}{61}+\frac{1}{85}+\frac{1}{97}< \frac{1}{5}+\frac{1}{10}+\frac{1}{10}+\frac{1}{40}+\frac{1}{40}+\frac{1}{40}+\frac{1}{40}=\frac{1}{5}+\frac{1}{5}+\frac{1}{10}=\frac{5}{10}=\frac{1}{2}\)\(\Rightarrow A< \frac{1}{2}\)
chứng minh rằng:
A=\(\frac{1}{5}+\frac{1}{14}+\frac{1}{28}+\frac{1}{44}+\frac{1}{61}+\frac{1}{85}+\frac{1}{97}< \frac{1}{2}\)