chứng minh: 1/1008x2014+1/1009x2013+....+1/2014x1008=1/1511x(1/1008+1/1009+...+1/2014)
cho A= 1/1x2+1/3x4+...+1/2013x2014 B=1/1008x2004+1/1009x2013+...+1/2014x1008
B=1/1008x2004+1/1009x2013+...+1/2014x1008
chứng tỏ rằng A/B là số nguyên
Ta có: A = 1 - 1/2 + 1/3 - 1/4 + ... +1/2013 - 1/2014
A = 1 + 1/2 + 1/3 + 1/4 +... + 1/2013 + 1/2014 - 2.(1/2 + 1/4 + ... + 1/2014)
A = 1 + 1/2 + 1/3 + 1/4 +... + 1/2013 + 1/2014 - (1 + 1/2 + 1/3 + ... + 1/1007)
A = 1/1008 + 1/1009 + ... + 1/2014
bạn viết lại B được ko
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2013.2014}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2013}-\frac{1}{2014}\)
\(A=1-\frac{1}{2014}\)
\(A=\frac{2013}{2014}\)
bài B thì đề khó hiểu quá
bn ghi lại đề rồi mình giải
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
cho A= 1/1x2+1/3x4+...+1/2013x2014
B=1/1008x2004+1/1009x2013+...+1/2014x1008
Hãy chứng tỏ rằng A/B là số nguyên
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.
Chứng minh rằng : \(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{2013.2014}=\frac{1}{1008}+\frac{1}{1009}+...+\frac{1}{2014}\)
Tính B=1/1008*2014 + 1/1009*2013 + 1/1010*2012 + ...+ 1/2014*1008
B=1/1008 * 2004+1/1009*2004+...+1/2014*1008
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=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2013}-\frac{1}{2014}\)
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