CM: 1/5+1/13+1/14+1/15+1/16+1/61+1/62+1/63<1/2
CMR: 1/5 + 1/13 +1/14 +1/15 +1/61 +1/62 + 1/63 < 1/2
chứng minh rằng s=1/5+1/13+1/14+1/15+1/61+1/62+1/63<1/2
CMR : 1/3+1/5+1/13+1/14+1/15+1/61+1/62+1/63<5/6
CMR : 1/3+1/5+1/13+1/14+1/15+1/61+1/62+1/63 < 5/6
chứng minh 1/5+1/13+1/14+1/15+1/61+1/62+1/63 < 1/2
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)
CTR
1/5+1/13+1/14+1/15+1/61+1/62+1/63<1/2
Đặt :
\(A=\dfrac{1}{5}+\dfrac{1}{13}+\dfrac{1}{15}+\dfrac{1}{61}+\dfrac{1}{62}+\dfrac{1}{63}\)
\(A=\dfrac{1}{5}+\left(\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{1}{15}\right)+\left(\dfrac{1}{61}+\dfrac{1}{62}+\dfrac{1}{63}\right)\)
Ta thấy :
\(\dfrac{1}{13}< \dfrac{1}{12};\dfrac{1}{14}< \dfrac{1}{12};\dfrac{1}{15}< \dfrac{1}{12}\)
\(\dfrac{1}{61}< \dfrac{1}{60};\dfrac{1}{62}< \dfrac{1}{60};\dfrac{1}{63}< \dfrac{1}{60}\)
\(\Rightarrow A< \dfrac{1}{5}+\left(\dfrac{1}{12}+\dfrac{1}{12}+\dfrac{1}{12}\right)+\left(\dfrac{1}{60}+\dfrac{1}{60}+\dfrac{1}{60}\right)\)
\(\Rightarrow A< \dfrac{1}{5}+\dfrac{1}{12}.3+\dfrac{1}{60}.3\)
\(\Rightarrow A< \dfrac{1}{5}+\dfrac{1}{4}+\dfrac{1}{20}\)
\(\Rightarrow A< \dfrac{1}{2}\rightarrowđpcm\)
~ Chúc bn học tốt ~
Chứng tỏ rằng : 1/5+1/13+1/14+1/15+1/61+1/62+1/63<1/2
TA có:
1/12>1/13
1/12>1/14
1/12>1/15
=>1/12.3=1/4>1/13+1/14+1/15
1/60>1/61
1/60>1/62
1/60>1/63
=>1/60.3=1/20>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
=>1/2> 1/5+1/13+1/14+1/15+1/61+1/62+1/63
Chứng minh S = 1/5 +1/13+ /14+1/15+1/61+1/62+1/63 < 1/2
Ta có:
\(\frac{1}{5}=\frac{1}{5}\)
\(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}
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)
CHỨNG MINH 1-(1/5 +1/13 +1/14+1/15+1/61 +1/62 +1/63) > 1/2
\(đpcm\Leftrightarrow\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}