CMR :1/1.2+1/3.4+...+1/2013.2014=1/1008+1/1009 +........+1/2013+1/2014
QG
Những câu hỏi liên quan
CMR: 1/1.2+1/3.4+1/5.6+1/7.8+...+1/2013.2014=1/1008+1/1009+1/1010+...+1/2013+1/2014
Chứng minh rằng
1/1.2 + 1/3.4 + 1/5.6 + 1/7.8 + ... + 1/2013.2014 = 1/1008 + 1/1009 + 1/1010 +...+ 1/2013+ 1/2014
$2015=5.13.31$2015=5.13.31
Ta có: $1.2.....1007=1.2...5....13.....31...1007\text{ chia hết cho }5.13.31=2015$1.2.....1007=1.2...5....13.....31...1007 chia hết cho 5.13.31=2015
$1008.1009.....2004=1008....\left(1010\right)....\left(1014\right)...\left(1023\right)....2004$1008.1009.....2004=1008....(1010)....(1014)...(1023)....2004
$=1008....\left(5.202\right)....\left(13.78\right)....\left(31.33\right)...2004\text{ chia hết cho }5.13.33=2015$=1008....(5.202)....(13.78)....(31.33)...2004 chia hết cho 5.13.33=2015
Do đó tổng 2 số trên chia hết cho 2015.
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Chứng minh rằng : \(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{2013.2014}=\frac{1}{1008}+\frac{1}{1009}+...+\frac{1}{2014}\)
(1/1008 + 1/1009 + 1/1010 +...+ 1/2014) : [1/2 + 1/(3.4) +1/(5.6) +...+ 1/(2013.2014)]=???
cho
A=1/1008+1/1009+.....+1/2014
B=1/1008*2014+1/1009*2013+......+1/2014*1008
hay chung minh rang B/A la so nguyen
A=1/1*2 + 1/3*4 + 1/5*6 + ... +1/2013*2014
B=1/1008*2014 + 1/1009*2013 + 1/1010*2012+ ... + 1/2014*1008
A=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2013}-\frac{1}{2014}\)
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Tính B=1/1008*2014 + 1/1009*2013 + 1/1010*2012 + ...+ 1/2014*1008
1/1*2+1/3*2+1/5*6+.....+1/2013*2014
-------------------------------------------------------
1/1008*2014+1/1009*2013+1/1010*2012+....1/2014*2018
Cho:
A= 1/1*2+1/3*4+1/5*6+...+1/2013*2014
B=1/1008*2014+1/1009*2013+...+1/2014*1008
Tính A/B