Cho B=1/5+1/6+1/7+...+1/17 .Chung to rang B<2
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chung to rang 1/5+1/6+1/7=...+1/16+1/17<2
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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BAI 1: chung to rang 175 + 244 + -1321 chia het cho 10
BAI 2:chung minh rang voi moi so tu nhien n :
a) 74n -1 chia het cho 5
b) 34n+1 +2 chia het cho 5
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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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
B = 1/22 + 1/32 + 1/42 + 1/52 + 1/62 + 1/72 + 1/82 < 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8
B = < 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8
B = < 1 - 1/8 < 1
=> đpcm
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cho a=1=1\2+1\3-1\4+1\5...+1\49-1\50.Chung to rang 7\12<4<5\6
chung minh rang B= 1/5+1/6+1/7+.....+1/19<11/6
biet A =717+17x3 -1 la so chia het cho 9.Co the su dung ket qua nay de chung to rang B= 718 +18x3-1 cung chia het cho 9 khong
chung minh rang 11^n+2+12^2n+1 chia het cho 133
chung minh rang A=(17^n+1)(17^n+2)chia het cho 3 voi moi n thuoc N
cho (2a+7b) chia het cho 3 ( a b thuoc N). chung to (4a+2b) chia het cho 3