cho A=1/2.3/4.5/6........99/100 va B=2/3.4/5.5/6.........100/101 so sanh A va B
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Cho M=1/2.3/4.5/6...99.100 va N=2/3.4/5.6/7.... 100/101 va N=2/3.4/5.6/7..100/101
a) So sanh M va N b) Tinh M.N c) So sanh M va 1/10
Cho a=1/2.3/4.5/6....99/100 và b=2/3.4/5.6/7....100/101 cmr:a<b
Vì
\(\frac{1}{2}< \frac{2}{3};\frac{3}{4}< \frac{4}{5};\frac{5}{6}< \frac{6}{7};...;\frac{99}{100}< \frac{100}{101}\)
\(\Rightarrow\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}< \frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{100}{101}\)
\(\Rightarrow a< b\)
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cho a=1/2.3/4.5/6. ... .99/100;b=2/3.4/5. ... .100/101;c=1/2.2/3.3/4. ... 98/99 a, so sánh a, b,c b,chứng minh a.c<a^2<1/100 c,chứng minh 1/15<a<1/10
M=1/2.3/4.5/6.…99/100; N=2/3.4/5.5/7….100/101
CMR M < NTìm tích của M.NCMR M < 1/10
A= 1/2.3/4.5/6...........99/100
B=2/3.4/5.6/7............100/101
1/So sánh: A và B, A2 và A.B
2/Chứng minh A<1/10
1/ ta co : 1/2<2/3 ; 3/4<4/5 ; 5/6<6/7 ;.......;99/100<100/101
=> A<B
Vi A<B nen A.A<A.B
2/ Vi A<B ( theo cau a) nen A.A<A.B=1/101
A.B<1/101 MA 1/101<1/100
=> A.B<1/100
A.A<1/10*1/10 . A<1/10
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A=1/2.3/4.5/6....99/100
B=2/3.4/5.6/7...100/101
a.so sánh Avà B,A mũ 2 và A.B
b.chứng tỏ A<1/10
ChoM=1/2.3/4.5/6.......99/100
N=2/3.4/5.6/7......100/101
a)Chứng minh M<N
b)M.N=?
H24
14 tháng 1 2018 lúc 13:34
Cho A=1.2+2.3+3.4+4.5+............+2017.2018 va B=2018 mu3/3 So sanh A va B
cho bài kham khảo nè :
A=1.2+2.3+3.4+4.5+...+2017.2018
=> 3A=1.2.3+2.3.3+3.4.3+4.5.3+...+2017.2018.3
3A=1.2.3+2.3(4-1)+3.4(5-2)+4.5(6-3)+...+2017.2018.(2019-2016)
3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+2017.2018.2019-2016.2017.2018
3A=(1.2.3+2.3.4+3.4.5+4.5.6+...+2017.2018.2019)-(1.2.3+2.3.4+3.4.5+...+2016.2017.2018)
=> 3A=2017.2018.2019 => \(A=\frac{2017.2018.2019}{3};B=\frac{2018^3}{3}=\frac{2018.2018.2018}{3}\)
Ta có: 2017.2019=2017(2018-1)=2017.2018+2017<2017.2018+2018=2018(2017+1)=2018.2018
=> 2017.2018.2019<2018.2018.2018
=> A<B
thank nha
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A=1.2+2.3+3.4+...+2017.2018
3A=1.2.3+2.3.3+3.4.3+...+2017.2018.3
3A=1.2.3+2.3.(4−1)+3.4.(5−2)+...+2017.2018.(2019−2016)
3A=1.2.3+2.3.4−1.2.3+3.4.5−2.3.4+...+2017.2018.2019−2016.2017.2018
⇒3A=2017.2018.2019
⇒A=2017.2018.20193
A=2017.2018.20193;B=201833=2018.2018.20183
A=2739315938;B=2739316611
⇒A<B
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\(A=1.2+2.3+3.4+4.5+............+2017.2018\)
\(3A = 1.2.3 + 2.3.4 +..............+ 2017.1018.3\)
\(3A = 1.2.3 + 2.3.(4-1) + .............. + 2017.2018.(2019-2016)\)
\(3A = 1.2.3 + 2.3.4 - 1.2.3 + ............. + 2017.2018.2019 - 2016.2017.2018\)
\(3A = 2017.2018.2019\)
\(A = \frac{2017.2018.2019}{3}\)
\(B =\frac {2018^3}{3}\)
đến đây ko bt lm
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Tính tổng
M=1/2.3/4.4/5.......99/100
N=2/3.4/5.5/6.....100/101
\(M=\frac{1}{2}.\frac{3}{4}.\frac{4}{5}...\frac{99}{100}\)
\(\Leftrightarrow M=\frac{1}{2}.\frac{3.4...99}{4.5...100}\)
\(\Leftrightarrow M=\frac{1}{2}.\frac{3}{100}\)
\(\Leftrightarrow M=\frac{3}{200}\)
\(N=\frac{2}{3}.\frac{4}{5}.\frac{5}{6}...\frac{100}{101}\)
\(\Leftrightarrow N=\frac{2}{3}.\frac{4.5...100}{5.6...101}\)
\(\Leftrightarrow N=\frac{2}{3}.\frac{4}{101}\)
\(\Leftrightarrow N=\frac{8}{303}\)
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