cho a=1/3*4/6*.....208/210
chung minh a<1/25
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Cho A= 1/3*4/6*7/9*10/12*...*208/210 . Chứng minh A<1/25
Cho A=(1/3)(4/6)(7/9)(10/12)....(208/210). Chứng minh A<1/25
Xét với mọi n > 2 , ta có \(\frac{n}{n+2}< \frac{n-1}{n}\) (vì \(n^2< n^2+n-2\))
Áp dụng : \(A=\frac{1}{3}.\frac{4}{6}.\frac{7}{9}.\frac{10}{12}...\frac{208}{210}< \frac{1}{3}.\frac{3}{4}.\frac{6}{7}.\frac{9}{10}...\frac{207}{208}\)
Suy ra : \(A^2< \frac{1.4.7.10...208}{3.6.9.12...210}.\frac{1.3.6.9...207}{3.4.7.10...208}=\frac{1}{210}.\frac{1}{3}=\frac{1}{630}< \frac{1}{625}=\left(\frac{1}{25}\right)^2\)
Do đó \(A< \frac{1}{25}\)
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Cho A=\(\frac{1}{3}.\frac{4}{6}.\frac{7}{9}.\frac{10}{12}...\frac{208}{210}\)
Chứng minh A<\(\frac{1}{25}\)
Cho A=\(\frac{1}{3}.\) \(\frac{4}{6}.\frac{7}{9}.\frac{10}{12}....\frac{208}{210}\)
Chứng minh rằng A<1/25
Cho A=\(\frac{1}{3}x\frac{4}{6}x\frac{7}{9}x.....x\frac{208}{210}\)
Chứng minh :A<\(\frac{1}{25}\)
Cho A=\(\frac{1}{3}.\frac{4}{6}.\frac{7}{9}...\frac{208}{210},CMR:A< \frac{1}{25}\)
a, 1+3+5+.............................+101
b, 2+4+6+..............................+208
c, 22+24+26+.........................+184
a/ 1 + 3 + 5 + ... + 101
= [(101 - 1) : 2 + 1] x (101 + 1) : 2
= 51 x 102 : 2
= 5202 : 2
= 2601
b/ 2 + 4 + 6 + ... + 208
= [(208 - 2) : 2 + 1] x (208 + 2) : 2
= 104 x 300 : 2
= 31200 : 2
= 15600
c/ 22 + 24 + 26+ ... +184
= [(184 - 22) : 2 + 1] x ( 184 + 22) : 2
= 82 x 206 : 2
= 16892 : 2
= 8446
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Bài 1: Tính nhanh;
A = 6/4 + 6/28 + 6/70 + 6/130 + 6/208
1/2A=1/2(6/4+6/28+6/70+6/130+6/208)
= 3/4+3/28+3/70+3/130+3/208
= 1-1/4+1/4-1/7+..................-1/16
=1-1/16
=15/16 => A=15/8
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Cho A=\(\frac{1}{3}.\frac{4}{6}\frac{7}{9}.\frac{10}{12}...\frac{208}{210}\)
CMR: \(\frac{1}{52}