A = 1/51 +1/52 + 1/53 + ... + 1/100
B = 1/1.2 + 1/3.4 + 1/4.5 + ... + 1/99.100
CMR A : B = 1
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Những câu hỏi liên quan
Cho A = 1/51 + 1/52+ 1/53 +...+ 1/100
B = 1/1.2 + 1/3.4 +1/5.6+...+ 1/99.100
A/ B = ?
a. A=1/51+1/52+1/53+...+1/100; B=1/1.2+1/3.4+...+1/99.100
so sánh A và B . biết A= 1/1.2 + 1/3.4 + 1/5.6 + ......+ 1 / 99.100
B = 2021/ 51 + 2021/52 + 2021/53 + .... + 2021/100
so sánh A và B . biết A= 1/1.2 + 1/3.4 + 1/5.6 + ......+ 1 / 99.100
B = 2021/ 51 + 2021/52 + 2021/53 + .... + 2021/100
=> A < B
chắc vại-.-
tui hok giỏi toán lém
cho A= 1/1.2 + 1/3.4 + 1/5.6 + ... + 1/99.100
a, chứng tỏ : A= 1/51 + 1/52 + 1/53 + ... + 1/99.100
b, chứng tỏ 7/12< A< 5/6
Cho A = 1/51 + 1/52+ 1/53 +...+ 1/100
B = 1/1.2 + 1/3.4 +1/5.6+...+ 1/99.100
A/ B = ? (chi tiết nha)
B=1/1.2+1/3.4+1/5.6+...+1/99.100
=1-1/2+1/3-1/4+1/5-1/6+...+1/99-1/100
=(1+1/3+1/5+...+1/99)-(1/2+1/4+1/6+...+1/100)
=(1+1/2+1/3+1/4+1/5+1/6+...+1/99+1/100)-2(1/2+1/4+1/6+...+1/100)
=(1+1/2+1/3+1/4+...+1/100)-(1+1/2+1/3+..+1/50)
=1/51+1/52+1/53+..+1/100 (1)
A=1/51+1/52+1/53+..+1/100 (2)
(1),(2)=> A/B=1
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Cho A = 1/1.2+1/3.4+1/5.6+...+1/99.100
a Chứng minh A= 1/51+1/52+1/53+...+1/100
b Chứng minh 7/12<A<5/6
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Cho A = 1/(1.2) +1/(3.4) +1/(5.6) +....+1/(99.100)
B= 2011/51 +2011/52+ 2011/53 +...+2011/100
CM: B/A là số nguyên
Tính B:C, biết: B=1/51+1/52+1/53+............+1/100
C= 1/1.2+1/3.4+1/5.6+..............+1/99.100
\(C=\frac{1}{1.2}+\frac{1}{3.4}+.....+\frac{1}{99.100}=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{99}-\frac{1}{100}=\left(1+\frac{1}{3}+....+\frac{1}{99}\right)-\left(\frac{1}{2}+\frac{1}{4}+.....+\frac{1}{100}\right)=\left(1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{99}+\frac{1}{100}\right)-2\left(\frac{1}{2}+\frac{1}{4}+.....+\frac{1}{100}\right)=\left(1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{99}+\frac{1}{100}\right)-\left(1+\frac{1}{2}+\frac{1}{3}....+\frac{1}{50}\right)=\frac{1}{51}+\frac{1}{52}+....+\frac{1}{100}\Rightarrow C:D=1\)
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