I = 1+1/3+1/5+......+1/2013+1/2015 chia cho 1/1.2015+1/3.2013+1/5.2011+.......+1/2011.5+1/2013.3+1/2015.1
TÝnh gi¸ trị của I
Những câu hỏi liên quan
1/1+1/3+1/5+.....+1/2013+1/2015 chia cho 1/1.2015+1/3.2013+1/5.2011+....+1/2011.5+1/2013.3+1/2015.1
1+1/3+1/5+...+1/2013+1/2015/1/1.2015+1/3.2013+1/5.2011+...+1/2013.3+1/2015.1
\(\dfrac{1+\dfrac{1}{3}+\dfrac{1}{5}+...+\dfrac{1}{2013}+\dfrac{1}{2015}}{\dfrac{1}{1.2015}+\dfrac{1}{3.2013}+\dfrac{1}{5+2011}+...+\dfrac{1}{2013.3}+\dfrac{1}{2015.1}}\)
giúp mình câu trên với mẫu là \(\dfrac{1}{1.2015}+\dfrac{1}{3.2013}+\dfrac{1}{5.2011}+...+\dfrac{1}{2013.3}+\dfrac{1}{2015.1}\)
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CHO :
\(S=\frac{1}{\sqrt{1.2015}}+\frac{1}{\sqrt{2.2014}}+\frac{1}{\sqrt{3.2013}}+..............+\frac{1}{\sqrt{2015.1}}\)
So sánh \(S\) với \(\frac{2.2014}{2015}\)
\(\sqrt{1.2015}\le\frac{2016}{2}\Rightarrow\frac{1}{\sqrt{1.2015}}\ge\frac{2}{2016}\)
=>S\(\ge\frac{2.1015}{2016}\)\(>\frac{2.2014}{2015}\)
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mách mk bài này đi
tính giá trị biểu thức sau a; -1 - 2 + 3 + 4 - 5 - 6 + 7 + 8 - 9 - 10 + 11 + 12-..........-2013 - 2014 + 2015 + 2016
b; {1/2 -1 } : {1/3-1} : { 1/4-1} : ......................: {1/99-1} : {1/100 -1
bn Nguyễn Huy Tú ngonhuminh Hoang Hung Quan mách mk
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nhìn mà khó hiểu quá viết hẳn phân số ra cho dễ nhìn đi
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Cho Sk=\(\frac{1}{\sqrt{1.2015}}+\frac{1}{\sqrt{2.2014}}+\frac{1}{\sqrt{3.2013}}+....+\frac{1}{\sqrt{k.\left(2016-k\right)}}vớik\in N^{sao},k\le2015\)
c/m Sk>k/1018
với \(a>0,b>0\)ta có \(\sqrt{a}.\sqrt{b}\le\frac{a+b}{2}\Rightarrow\frac{1}{\sqrt{a}.\sqrt{b}}\ge\frac{2}{a+b}\)
từ đó ta có : \(\frac{1}{\sqrt{k\left(2016-k\right)}}\ge\frac{2}{k+2016-k}\ge\frac{2}{2016}=\frac{1}{1008},\)với mọi \(k\in N^{\cdot}\)
Suy ra \(S_k\)\(\ge k.\frac{1}{1008}>k.\frac{1}{1018}\)(đpcm).
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Xem thêm câu trả lời
1.giá trị của x lớn hơn 1 thỏa mãn 1/2+1/3< x< 3 - 1/3
2.2012+2013+2014/2014 nhân 2015 -2016
3. giá trị của a để số 1a783 chia hết 9 chia cho 5 dư 3
Tính:
a) \(A=1+\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+\dfrac{1}{4}\left(1+2+3+4\right)+...+\dfrac{1}{2013}\left(1+2+...+2013\right)\)b) \(B=\dfrac{1-3}{1\cdot3}+\dfrac{2-4}{2\cdot4}+\dfrac{3-5}{3\cdot5}+\dfrac{4-6}{4\cdot6}+...+\dfrac{2011-2013}{2011\cdot2013}+\dfrac{2012-2014}{2012\cdot2014}+\dfrac{2013-2015}{2013\cdot2015}\)Giúp mình với!
\(A=1+\dfrac{\dfrac{\left(1+2\right).2}{2}}{2}+\dfrac{\dfrac{\left(1+3\right).3}{2}}{3}+...+\dfrac{\dfrac{\left(1+2013\right).2013}{2}}{2013}\)
\(A=1+\dfrac{\dfrac{3.2}{2}}{2}+\dfrac{\dfrac{4.3}{2}}{3}+...+\dfrac{\dfrac{2014.2013}{2}}{2013}\)
\(A=1+\dfrac{3}{2}+\dfrac{2.3}{3}+...+\dfrac{1007.2013}{2013}\)
\(A=1+\dfrac{3}{2}+2+\dfrac{5}{2}...+1007\)
\(2A=2+3+4+5+6+...+2012+2013+2014\)
\(2A=\dfrac{\left(2+2014\right).2013}{2}\)
\(A=\dfrac{2016.2013}{4}=504.2013\)
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\(B=\dfrac{-2}{1.3}+\dfrac{-2}{2.4}+...+\dfrac{-2}{2012.2014}+\dfrac{-2}{2013.2015}\)
\(-B=\dfrac{2}{1.3}+\dfrac{2}{2.4}+...+\dfrac{2}{2012.2014}+\dfrac{2}{2013.2015}\)
\(-B=\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{2013.2015}\right)+\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{2012.2014}\right)\)
\(-B=\left(\dfrac{3-1}{1.3}+\dfrac{5-3}{3.5}+...+\dfrac{2015-2013}{2013.2015}\right)+\left(\dfrac{4-2}{2.4}+\dfrac{6-4}{4.6}+...+\dfrac{2014-2012}{2012.2014}\right)\)
\(-B=\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{2013}-\dfrac{1}{2015}\right)+\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}+...+\dfrac{1}{2012}-\dfrac{1}{2014}\right)\)
\(-B=\left(1-\dfrac{1}{2015}\right)+\left(\dfrac{1}{2}-\dfrac{1}{2014}\right)\)
\(-B=\dfrac{2014}{2015}+\dfrac{2012}{2014.2}=\dfrac{2014^2+1006.2015}{2015.2014}\)
\(B=\dfrac{2014^2+1006.2015}{-2015.2014}\)
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1/1+1/3+1/5+...+1/2013+1/2015/1/1*2015+1/3*2013+1/5*2011+...+1/2011*5+1/2013*3+1/2015*1