Câu 1
Cho A= (1+2012/1)(1+2012/2)...(1+2012/1000)
B=(1+1000/1)(1+1000/2).....(1+1000/2012)
Tính \(\frac{A}{B}\)
Câu 2
cho E = 1/1.2 + 1/3.4 +1/5.6 +....+1/2013.2014
F= 1/1008.2014 + 1/1009,2013 +....+1/2014.1008
Tính \(\frac{E}{F}\)
Những câu hỏi liên quan
Câu 1 : TínhA 1/2 + 1/3 + 1/4 +...+1/300B 2999/1 + 2998/2 + 2997/3 +...+1/2999Tính frac{A}{B}Câu 2C (1+2012/1)(1+2012/2)....(1+2012/1000)D(1+1000/1)(1+1000/2)(1+1000/3)...(1+1000/2012)Tính frac{C}{D}Câu 3Cho E1/1.2 + 1/3.4 + 1/5.6 +...+1/2013/2014F1/1008/2014 + 1009/2013 +.....+1/2014.1008Tính frac{E}{F}
Đọc tiếp
Câu 1 : Tính
A= 1/2 + 1/3 + 1/4 +...+1/300
B= 2999/1 + 2998/2 + 2997/3 +...+1/2999
Tính \(\frac{A}{B}\)
Câu 2
C= (1+2012/1)(1+2012/2)....(1+2012/1000)
D=(1+1000/1)(1+1000/2)(1+1000/3)...(1+1000/2012)
Tính \(\frac{C}{D}\)
Câu 3
Cho E=1/1.2 + 1/3.4 + 1/5.6 +...+1/2013/2014
F=1/1008/2014 + 1009/2013 +.....+1/2014.1008
Tính \(\frac{E}{F}\)
Câu 1:
B = \(\frac{2999}{1}+\frac{2998}{2}+\frac{2997}{3}+...+\frac{1}{2999}\)
= \(\frac{3000-1}{1}+\frac{3000-2}{2}+\frac{3000-3}{3}+...+\frac{3000-2999}{2999}\)
= \(\left(\frac{3000}{1}+\frac{3000}{2}+\frac{3000}{3}+...+\frac{3000}{2999}\right)-\left(\frac{1}{1}+\frac{2}{2}+\frac{3}{3}+...+\frac{2999}{2999}\right)\)
= \(3000+3000.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2999}\right)-2999\)
= \(3000\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2999}\right)+\frac{3000}{3000}\)
= \(3000\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{3000}\right)\)
\(\Rightarrow\frac{A}{B}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{3000}}{3000\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{3000}\right)}=\frac{1}{3000}\)
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C=2013/1*2014/2*2015/3*...*3012/1000
C=2013*2014*2015*...*3012/1*2*3*...*1000
D=1001/1*1002/2*1003/3*...*3012/2012
D=1001*1002*...*3012/1*2*...*2012
Suy ra C/D=2013*2014*2015*...3012*1*2*...*2012/1*2*3*...*1000*1001*1002*...*3012
( Nhân đảo ngược)
Vậy C/D=1
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tính B=[(1+2012/1)+(1+2012/2)+(1+2012/3)+...+(1+2012/1000)]:[(1+1000/1)+(1+1000/2)+...+(1+1000/2012)]
tính: B=[(1+2012/1)+(1+2012/2)+....+(1+2012/1000)]:[(1+1000/1)+(1+1000/2)+....+(1+1000/2012)]
.
(1+2012/1)(1+2012/2)(1+2012/3).......(1+2012/1000)
(1+1000/1)(1+1000/2)..........(1+1000/2012)
Tính A
tính: B=[(1+2012/1)+(1+2012/2)+....+(1+2012/1000)]:[(1+1000/1)+(1+1000/2)+....+(1+1000/2012)]
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Tính: A=((1+2012)(1+2013).....(1+2012/100))/((1+1000/1)(1+1000/2).....(1+1000/2012)
Tinh [(1+2012/1)*(1+2012/2)*(1+2012/3)*...*(1+2012/1000)]/[(1+1000/1)*(1+1000/2)*(1+1000/3)*...*(1+1000/2012)]
Rút gọn :
a/ \(A=\frac{\frac{1}{19}+\frac{2}{18}+\frac{3}{17}+...+\frac{19}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{20}}\)
b/ \(B=\frac{\left(1+\frac{2012}{1}\right)\left(1+\frac{2012}{2}\right)...\left(1+\frac{2012}{1000}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right)...\left(1+\frac{1000}{2012}\right)}\)
Tính:
(1 + 2012/1)(1 + 2012/2)....(1 + 2012/1000)
(1 + 1000/1)(1 + 1000/2)....(1 + 1000/2012)