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
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
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 \(\dfrac{1}{1.2015}+\dfrac{1}{3.2013}+\dfrac{1}{5.2011}+...+\dfrac{1}{2013.3}+\dfrac{1}{2015.1}\)
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\(\ge\frac{2.1015}{2016}\)\(>\frac{2.2014}{2015}\)
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).
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
giúp mk câu này nhé!
1.2015 + 2.2014 + 3.2013 +......+ 2015.1 / 1.2 + 2.3 + 3.4 +.......+ 2015.2016
ai nhanh và đúng nhất mk tk
a)1 N chia 7 dư 5 chia 13 dư 4.Nếu đem số đó chia cho 91 dư bao nhiu?
b)Tìm số tự nhiên x bít:1/3+1/6+1/10+.........+2/x(x+1)=2013/2015
c)CMR 1/2-1/4+1/8-1/16+1/32-1/64<1/3
(1/2012+1/2013-1/2014)/(5/2012+5/2013-5/2014)-(2/2103+2/2014-2/2015)/(3/2013+3/2014-3/2015)
\(\frac{\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}}{\frac{5}{2012}+\frac{5}{2013}-\frac{5}{2014}}-\frac{\frac{2}{2013}+\frac{2}{2014}-\frac{2}{2015}}{\frac{3}{2013}+\frac{3}{2014}-\frac{3}{2015}}\)
=\(\frac{\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}}{5\left(\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}\right)}-\frac{2\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}\right)}{3\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}\right)}=\frac{1}{5}-\frac{2}{3}=\frac{3}{15}-\frac{10}{15}=-\frac{7}{15}\)