a=1/1+3+1/1+3+5+1/1+3+5+7+......+1/1+3+5+7+...+2017
chung minh a<3/4
K
Khách
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Những câu hỏi liên quan
NY
13 tháng 12 2018
a) A=21+22+23+...+22010
A=(21+22)+(23+24)+.....+(22009+22010)
A=(21x3)+(23x3)+.....+(22009x3)
A=3x(21+23+.......+22009)
Vậy A chia hết cho 3.
NHỮNG CÂU CÒN LẠI BẠN LÀM TƯƠNG TỰ !
LT
0
TM
1
17 tháng 4 2017
Ta có :
\(A=\dfrac{1}{1+3}+\dfrac{1}{1+3+5}+...........+\dfrac{1}{1+3+.....+2013}\)
\(A=\dfrac{1}{\dfrac{\left(1+3\right).2}{2}}+\dfrac{1}{\dfrac{\left(1+5\right).3}{2}}+.........+\dfrac{1}{\dfrac{\left(1+2013\right).1007}{2}}\)
\(A=\dfrac{2}{2.4}+\dfrac{2}{3.6}+\dfrac{2}{4.8}+...........+\dfrac{2}{1007.2014}\)
\(A=\dfrac{1}{2.2}+\dfrac{1}{3.3}+\dfrac{1}{4.4}+..........+\dfrac{1}{1007.1007}\)
\(\Rightarrow A< \dfrac{1}{2.2}+\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+......+\dfrac{1}{1006.1008}\right)\)
\(\Rightarrow A< \dfrac{1}{4}+\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...........+\dfrac{1}{1006}-\dfrac{1}{1007}\right)\)
\(\Rightarrow A< \dfrac{1}{4}+\left(\dfrac{1}{2}-\dfrac{1}{1007}\right)\)
\(\Rightarrow A< \dfrac{1}{4}+\dfrac{1}{2}=\dfrac{3}{4}\) \(\rightarrowđpcm\)
~ Chúc bn học tốt ~
21 tháng 4 2017
A=1/(1+3)+1/(1+3+5)+1/(1+3+5+7)+...+1/(1+3+5+7+...+2017)
A=1/2^2+1/3^2+1/4^2+...+1/1009^2
2A=2/2^2+2/3^2+2/4^2+...+2/1009^2
Ta co :(x-1)(x+1)=(x-1)x+x-1=x^2-x+x-1=x^2-1<x^2
suy ra 2A<2/(1*3)+2/(3*5)+2/(5*7)+...+2/(1008*1010)
suy ra 2A <1-1/3+1/3-1/5+1/5-1/7+...+1/1008-1/1010
suy ra 2A<1-1/1010
suy ra 2A<2009/2010<1<3/2
suy ra 2A <3/2
suy ra A <3/4 (dpcm)
nho k cho minh voi nha
F
2
B
6 tháng 5 2021
A = \(\dfrac{1}{1+3}\) + \(\dfrac{1}{1+3+5}\) + \(\dfrac{1}{1+3+5+7}\) + ... + \(\dfrac{1}{1+3+5+7+...+2021}\)
\(\Leftrightarrow\) A = \(\dfrac{1}{\dfrac{\left(1+3\right).2}{2}}\) + \(\dfrac{1}{\dfrac{\left(1+5\right).3}{2}}\) + \(\dfrac{1}{\dfrac{\left(1+7\right).4}{2}}\) + ... + \(\dfrac{1}{\dfrac{\left(1+2021\right).1011}{2}}\)
= \(\dfrac{2}{2.4}\) + \(\dfrac{2}{3.6}\) + \(\dfrac{2}{4.8}\) + ... + \(\dfrac{2}{1011.2021}\)
= \(\dfrac{1}{2.2}\) + \(\dfrac{1}{3.3}\) + \(\dfrac{1}{4.4}\) + ... + \(\dfrac{1}{2021.2021}\)
A < \(\dfrac{1}{4}\) + ( \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + ... + \(\dfrac{1}{2020.2021}\) )
< \(\dfrac{1}{4}\) + ( \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + ... + \(\dfrac{1}{2020}\) - \(\dfrac{1}{2021}\) )
< \(\dfrac{1}{4}\) + ( \(\dfrac{1}{2}\) - \(\dfrac{1}{2021}\) ) < \(\dfrac{1}{4}\) + \(\dfrac{1}{2}\) = \(\dfrac{3}{4}\)
Kiểu như vậy hả ?
D
0
NM
20 tháng 7 2023
a) -1/24 - [ 1/4 - ( 1/2 - 7/8 )]
= -1/24 - [ 1/4 +3/8 ]
= -1/24 - 5/8
= -2/3.
DT
20 tháng 7 2023
a) -1/24 - [ 1/4 - ( 1/2 - 7/8 )]
= -1/24 - [ 1/4 +3/8 ]
= -1/24 - 5/8
= -2/3.
A=1/2^2+1/3^2+....+1/1009^2
2A=2/2^2+2/3^2+...+2/1009^2
Ta có : (x-1).(x+1)=(x-1).x+x-1=x^2-x+x-1=x^2-1<x^2
2A<2/1.3+2/3.5+2/5.7+...+2/1008.10010
2A<1-1/3+1/3-1/5+...+1/1008-1/1010
2A<1-1/1010
2A<1009/1010<1<3/2
2A<3/2
A<3/4
ĐPCM
Nhớ cho mình nha!