A=1+2^2+2^4+.......+2^2014
So sánh A với 2016
K
Khách
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Những câu hỏi liên quan
NT
1
18 tháng 8 2016
A=\(\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}.....\frac{2016^2-1}{2016^2}\)
A=\(\frac{\left(2+1\right)\left(2-1\right)}{2^2}.\frac{\left(3+1\right)\left(3-1\right)}{3^2}......\frac{\left(2016+1\right)\left(2016-1\right)}{2016^2}\)
A=\(\frac{3.4......2017}{2.3....2016}.\frac{1.2...2015}{2.3...2016}\)
A=\(\frac{2017}{2}.\frac{1}{2016}\)
A=\(\frac{2017}{2.2106}>\frac{1}{2}\)
Vậy A\(>\frac{1}{2}\)
S
4
PT
0
TQ
1
NL
10 tháng 5 2016
A=\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2014.2015.2016}\)
A=\(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2014.2015}-\frac{1}{2015.2016}\right)\)
A=\(\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2015.2016}\right)\)
A=\(\frac{1}{4}-\frac{1}{2015.2016.2}\)\(\Rightarrow A<\frac{1}{4}\)
TP
0
T
0
DV
10
TM
11 tháng 5 2016
Ta có: \(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2016}}\)
\(\Rightarrow2A=2\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+..+\frac{1}{2^{2016}}\right)\)
\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2015}}\)
\(\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2015}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2016}}\right)\)
\(\Rightarrow A=1-\frac{1}{2^{2016}}\)
\(\Rightarrow A<1\left(đpcm\right)\)
HP
11 tháng 5 2016
\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.....+\frac{1}{2^{2016}}\)
=>\(2A=1+\frac{1}{2}+\frac{1}{2^2}+.....+\frac{1}{2^{2015}}\)
=>\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{2015}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{2016}}\right)\)
=>\(A=1-\frac{1}{2^{2016}}\)
Vậy \(A=1-\frac{1}{2^{2016}}\)
AL
2
BT
9 tháng 5 2017
2A=2/1.2.3 + 2/2.3.4 + 2/3.4.5 + ...+2/2014.2015.2016
Ta có: 2/1.2.3=1/1.2-1/2.3; 2/2.3.4=1/2.3-1/3.4; 2/3.4.5=1/3.4-1/4.5; ....; 2/2014.2015.2016=1/2014.2015-1/2015.2016
=> 2A=1/1.2-1/2015.2016
=> 2A < 1/2 => A < 1/4
2A=2+2^2+...+2^2014
2A-A
=>A=2^2015-1
Mà:2^11.2^2004-1=2048.2^2004-1
=>A>2016