cho B=1/4+1/5+1/6+...+1/19. Chung to rang B>1
MINH CAN GAP
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Cho B=1/4+1/5+1/6+...+1/19.Hay chung to rang B>1
Ta có:\(\frac{1}{5}>\frac{1}{6}>...>\frac{1}{19}\)
=>B=\(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}>\frac{1}{4}+\frac{1}{19}+\frac{1}{19}+...+\frac{1}{19}\)(15 lần 1/19)
=>B>1/4+15/19=79/76>1
=>B>1
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1)chung to rang so nguyen to p;p>5 khi chia cho 6 chi co the du 1 hoac 5
2)chung minh rang neu p va p+2 la so nguyen to lon hon 3 thi p+1 la mot hop so
cac an giai giup minh minh dang can gap
ai giai nhanh minh tick cho
Cho B=\(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}\)Hay chung to rang B>1
cho \(B=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}\)
chung to rang B >1
Ta có: 1/4+1/5+...+1/10>1/10.7=7/10
1/11+1/12+...+1/19>1/20.9=9/20
Kết hợp lại ta có B= 1/4+1/5+1/6+...+1/19>7/10+9/20=23/20>1.Vậy B>1
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ta co 1/4+1/5+......+1/10>1/10.7=7/10
1/11+1/12+.....1/19>1/20.9=9/20
kết hợp lại ta có mB=1/4+1/5+1/6+......1/19>7/10+9/20=23/20>1 vậy B>1
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ta có:
1/4>1/10
1/5>1/10
1/6>1/10
1/7>1/10
1/8>1/10
1/9>1/10
=>1/4 +1/5+1/6+1/7+1/8+1/9>1/10*6
=>1/4+1/5+1/6+1/7+1/8+1/9+1/10>1/10*7
=>1/4+1/5+1/6+...+1/19>1/10*7+1/11+1/12+...+1/19
=>1/4+1/5+1/6+...+1/19>7/10+1/11+1/12+...+1/19
mà ta thấy:
1/11>1/20
1/12>1/20
1/13>1/20
1/14>1/20
1/15>1/20
...
1/19>1/20
=>1/11+1/12+1/13+...+1/19>1/20*9
=>1/4+1/5+1/6+...+1/19>1/10*7+1/20*9
=>B>7/10+9/20
=>B>23/20=1.15>1
=>B>1(dpcm)
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bai 1 ; chung to rang ;
a, 10 mu 5 + 35 chia het cho 5 va 9
b, 10 mu 5 + 98 chia het cho 2 va 9
giup minh gap di ai nhanh minh nhan like mai minh can roi
Cho 10^k - 1 chia het cho 19 . Chung minh rang
10^2k -1 chia het cho 19
10^3k -1 chia het cho 19
Giup minh nha dang can gap trong ngay hom nay
10 mũ 2 nhân k hay 10 mũ 2k nói rõ đi mk giải cho
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chung to rang B=1/2^2+1/3^2+1/4^2+1/5^2+1/6^2+1/7^2+1/8^2<1
ai lam duoc minh tick cho
Ta thấy:
\(\frac{1}{2^2}< \frac{1}{1.2}\)
\(\frac{1}{3^2}< \frac{1}{2.3}\)
........................
\(\frac{1}{8^2}< \frac{1}{7.8}\)
\(\Rightarrow B< \frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{7.8}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{7}-\frac{1}{8}=1-\frac{1}{8}< 1\)
Vậy B < 1
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cho A=1/3^2-1/3^4+1/3^6-1/3^8+...+1/3^2014-1/3^2016 . Chung minh rang A < 0,1 . Hay tong quat bai toan
Minh dang can gap
1/3^2-1/3^4=3^2/3^4-1/3^4=8/3^4
1/3^6-1/3^8=1./3^4.8/3^4=8/3^8
1/3^2014-1/3^2016=8/3^2004
A/8=1/3^4+1/3^8+...+..1/3^2004
A/(8.3^4)=1/3^8+1/3^12+..+1/3^2008
A(1/8-1/(8.3^4)=1/3^4-1/3^2008=(3^2004-1)/3^2008
10.A(1/3^4)=...
10A=(3^2004-1)/3^2004<1
vậy A<1/10=0,1
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Cho B=1/5+1/6+1/7+...+1/17 .Chung to rang B<2